As for the Amalfi coast, IMO Ravello, Amalfi, Positano are very nice for chilling out and relaxing.

For those of you who helped me with researching places for our vacation in earlier forums - THANK YOU! The tickets are BOOKED and we are going! We are going in late May/early June and spending 3 nights in Rome, 3 nights in Ravello, 3 nights in Mykinos, 4 nights in Santorini and 1 night in Athens. We are VERY excited! Of course now that we have the schedule down, we need some help with details. We are using the travel agent who helped us with our honeymoon, but I have gotten lots of information from several different people and wanted help figuring out what areas to stay in, etc. etc. With that being said - please see below:
FIRST: In Rome, our travel train travel agent gave us the first two suggestions. The first one is more expensive and the second train travel one looks very nice, is in a great location for sightseeing, but is less expensive, so that is probably what we are leaning towards. The problem is - my mother is OBSESSED train travel with the hotel/area that she and my dad stayed in when they were in Rome. The hotel they stayed in is link 3 and is in Travestere which I hear is about a 10 to 15 minute walk from the center of Rome. My question is: Where would a 30 year old couple who wants to sight see and eat great dinners want to stay? Any dinner suggestions are welcome as well!
SECOND: In Ravello - we hear that Capri and the town of Amalfi are both within a 15 to 20 minute drive. Does anyone have any suggestions for "must see" attractions there? Any good hikes / walks? Would you say rent a car or take a taxi? Any amazing restaurants that we NEED to eat in?
Renting a car on the AC in high season is a really bad idea - especially since few hotels train travel have any parking available. Travel should be by taxi or SITA bus - but be prepared for traffic along the coast highway to be about 10 mph - and buses are often full to overflowing.
How do you plan to get to Mykonos? That will not be easy and may take an entire day--if you get an early start. I suggest you get a good guide book for the AC, and check on flights fom Naples to Athens. This trip is all about travel logistics.
HOW TO GET THERE: You have to want to it may not be easy. The best option is to land in Naples, but that is not always feasible. Most travelers access it from Rome by train to Naples a trip of less than two hours. Once in Naples, you have a choice. The local commuter train, Circumversuviana, leaves from the same train station and takes about an hour to SORRENTO, with a possible stop at Pompeii Scavi to see the famed ruins. However, to access any of the coastal towns you must then take a SITA bus or a taxi.
WHERE TO LOCATE WHAT TO SEE: Ah, what not to see? This is the most stunning scenery in all of Italy---be sure to pack the camera. Your daily activities will be somewhat determined by your location. SORRENTO is really on the Bay of Naples and not the Amalfi Coast [AC], but is the most convenient location for day trips to Pompeii and the Isle of Capri. train travel The town is larger relatively flat. In contrast, POSITANO is the most spectacular village on the AC but is almost vertical and a real challenge for your legs.
Hotel choices in Positano should be evaluated by their location in town relative to the beach or position train travel on the hill above the beach. AMALFI RAVELLO are other popular destinations but are further down the coast.
I also was a bit surprised by the travel involved with the places you are going as I do think some of the logistics from Italy to Greece will be more than I would want to try to plan (or experience) in your time frame. train travel But hopefully the travel agent has it so you will not be too frazzled. I do love your choices apart from the logistics involved.
Back to Rome - I think staying in Trastvere will be fine - true, it is not tourist ground train travel zero, but you can get around to those places easily enough on public transportation. train travel When we visit Rome we love to go to that area, usually just for dinner but it would be fine to stay there - LOTS of pleasant, mom and pop restaurants and some nice outdoor piazzas as well.
As for the Amalfi coast, IMO Ravello, Amalfi, Positano train travel are very nice for chilling out and relaxing. If you want to sightsee the area, Sorrento might be better. Capri can be a nice (long) day trip but I like to spend a few nights there. There is enough to do for a very pleasant 3 day stay so that could be your option for that part of your trip.
I am not sure Ravello is the best choice for your stay on the Amalfi Coast. It is actually not on the water, but is a 20 minute bus or taxi ride WAY up the hill from Amalfi. So if you want to see anything other than Ravello, you need to bus or taxi down to Amalfi, then get to your next destination train travel from there.
train travel With your limited time, and given the fact you are flying out of Naples, I would suggest staying in Positano and sightseeing from there. You can take the train from Rome to Salerno and then a ferry (if they are running) from Salerno to Positano. If the ferries are not running, then you can take the train from Rome to Salerno and then take the bus to Positano. Or you can take the train from Rome to Naples, then a separate train to Sorrento and then a bus or driver to Positano (or driver from Naples to Positano). If you search this board you will find TONS of posts on how to get from Rome to the Amalfi Coast.
Getting from Rome to your hotel in Pos will take most of the morning, so after you check in you can have a leisurely lunch and spend the afternoon wandering the town. Highly train travel recommend a tour with Christine at www.discoverpositano.com . Great way to learn the history of Positano. I had a great dinner at Tre Sorelle right on the beach - really good pizza and pasta.
The next day you can take the ferry to Capri and spend the day sightseeing and then back to Pos. Take the bus or a taxi and have cocktails on the terrace at Hotel San Pietro at sunset and then have dinner back in Pos - and maybe a little dancing at Music on the Rocks.
train travel On your last day on the AC, you can take the bus to Amalfi and spend the day exploring Amalfi and Ravello. Depending on the bus schedule, you may be able to have dinner in Amalfi. We had dinner at Lido Azzuro in Amalfi and then had a driver take us back to Positano.
The next morning you will have to leave Pos VERY early to catch your 9 a.m. flight - you have to be at the Naples airport by 7 a.m. at the very latest, so I would book a driver to take you from Pos to the airport, leaving plenty of time for traffic - at least 1.5 hours, which means you are leaving your hotel at 5:30 a.m.
You DO NOT want to rent a car on the AC - terrible traffic and parking is scarce and expensive. You will be fine with the ferries and buses. Hopefully you will have some time for relaxing on a beach when you get to Greece!
Bob doesn't seem to like staying in Amalfi, which many of us prefer because it's more of a real Italian town. Ravello is too remote a place to stay. It's great to visit though, wonderful views back down to the coastline.
And if you haven't driven in Italy before, I wouldn't start on the Amalfi coast. The road is carved into the cliff side, very narrow with lots of hairpin turns -- and with the Mediterranean a steep drop below. Parking along the coast is very hard to find and expensive. You can travel along the coast by bus or boat.
Also for food/life in Italy stuff, check out Katie Parla www.parlafood.com and Elizabeth Minchilli www.elizabethminchilliinrome.com Both are Rome based ex-pats they also have smart phone apps that are great for finding restaurants.
I stayed at the Hotel Majestic in 1999. It was a nice hotel, but the mattress was terrible. train travel However, train travel they have renovated since then. I like the Via Veneto location, though. Last time I was in Rome I stayed at the Excelsior, also on Via Veneto.
I agree with the recommendations about not staying in Ravello but rather, maybe, Positano. I would try to go to Ravello to visit, though. It is lovely, and the views from Villa Rufolo, and especially Villa Cimbrone, are stunning.
can't help with the amalfi section, and i've never stayed at any of your rome selections, mainly because they are none of them close enough to the centre for me. the first two are more or less in the same place near the borghese gardens, thus quite a long way from most places you'll want to be for a first visit, and the 3rd one, although technically train travel in Trastevere is not close enough to the centre to avoid a lot of walking.
I agree with mimar and would go for somewhere near the pantheon or piazza navona. there's train travel a recent thread on just that subject or www.venere.com is very good at showing you what's available for your dates in different areas of a city. you can also select train travel by facility and price. then tell your travel agent where you want to go.
We were using the car to drive to Pompeii, to Naples and to towns down the coast. (We didn't have any problems with driving - but we are used to NYC - that is searching for a place to park and parallel parking in places barely larger than the car - no mall type parking.
On hotels in Rome, option 2 on the via Veneto, that would be further that I'd want to be. We enjoy visiting the Piazza Navona, Campo dei' Fiori, Pantheon almost every evening for drinks and people-watching, so we prefer to be closer to that part of the city. We've stayed several times at Residenza Canali ai Coronari, which may be a little below the price point you're looking for.
On our last visit to Rome, this fall, we stayed in Trastevere, at Relais le Clarisse, because I love that area. It was a delightful area to be in, but for us, it was a little too far. It was 20 min. from our hotel, walking, up to Piazza Navona. And there is a tram you could take, but it doesn't train travel go the whole way up to the Piazza Navona area. The hotel you're considering in Trastevere would be a bit further from the central part of historic Rome than the place we stayed. That being said, I felt that Trastevere was less touristy, and had lots of fun cafes and restaurants. On our last day, also, we stopp