Closest are the Onyx, Bulfinch, and Holiday Inn Express (was called Hotel @ The Garden for part of 2

Hotels for a Fleet Center Concert (TD Garden)
Closest are the Onyx, Bulfinch, and Holiday Inn Express (was called Hotel @ The Garden for part of 2010 when a window payless car and van rental replacement project was underway). Being the very closest can have pros and cons, as the area around the Garden (Fleet Center) payless car and van rental has lots of bars and clubs, and can get noisy - although the crowd after a concert will be very different than, for example, after a Bruins game.
Still, they're all an easy walk away, with the Bulfinch being very slightly farther than the other 2. They're all in what you would call the "boutique" category - less than 150 rooms. If you're driving down from Maine, I believe that the Holiday payless car and van rental Inn Express and the Onyx offer valet parking only (probably offsite). The Bulfinch has on-site parking - currently (2011) $42 for valet, and $30 for self-park if you don't need to go in and out while you're here.
You can find information about all of these hotels here, along with links to check rates from a variety of booking agencies, and ratings from other visitors. You should be able to still find good deals on rates in April.
There's also a regular large Holiday Inn about 4 blocks payless car and van rental away toward Beacon Hill, right across from Mass General. Large parking garage is underneath the hotel, and easy to get to from Storrow Drive (exit onto Cambridge St). It's also about a 5-minute walk from Beacon Hill. Use the link above to find more info about it.
Another option is the Millennium Bostonian. It's a little farther than the others, but very nice - close to Faneuil Marketplace. payless car and van rental Be sure to look for special deals and packages here as well - they usually have some good ones. Boston spring flowers photo gallery