The Hotel Commonwealth the closest, nice hotel near Fenway Park (just across the little bridge in Kenmore Square). Also, if you stay there (or even if you don't), you should hit the Island Creek Oyster Bar. Great atmosphere, cool interior, and great food.
There are a lots of other really nice hotels in the Back Bay (The Eliot Hotel is close to Kenmore Square too) and then there are Hyatts and Marriotts and other nice, well-known brands, such as the Four Seasons and the Ritz and so on -- all a short cab ride away from Fenway Park.
Boston has so many great hotels! Plus, it's such a small and manageable city which makes it very easy to walk or take public transportation to get where you want to go.
If the main purpose of your trip is to go to Fenway Park , and if it's very important that you stay right nearby, then The Eliot Hotel and Hotel Commonwealth are both good choices. However, I personally wouldn't say that'll put you "where all the action is."
The Fenway area is fun and home to some great bars, but if you're visiting Boston for more than a trip to Fenway Park, I would stay in a different part of the city and just take the T (Boston's subway/light rail) to Fenway for the game.
That being said, here are some hotels that'll put you right in Downtown Boston and in/near where all the action is.
XV Beacon Hotel - A amazing hotel with incredible design. It'll put you right on the edge of Beacon Hill, The Boston Common, and a few minute walk to Faneuil Hall and The North End.
Nine Zero Hotel - There are fantastic views from upper rooms, great design, and located near everything described in the above.
Taj Boston - This place is sophisticated and really incredible. It's located at the beginning of Newbury Street and right on the beautiful Public Garden.
W Boston - It's a W so you know what you'll get here (trendy, mood lights, etc.) It's in the Theater District and pretty much across the street from Chinatown.
The Fairmont Copley Plaza Hotel Boston - This is a Boston landmark (it's an absolutely amazing building). Plus it'll bring you a little closer to Fenway.
Beacon Hill Hotel (25 Charles St, Boston, Massachusetts 02114) - Great if you're going with someone special and looking for something really small and unique. Plus it's right on Charles Street in Beacon Hill (which is one of the nicest streets/areas of any city in the country).
To get to Fenway Park from any of these hotels, all you'll have to do is hop on on outbound B, C, or D Green Line train and get off at Kenmore. It should take about 10-20 minutes.
Another thing to keep in mind if you're in the Fenway area late after a game, is that the T closes around 12:30am. Boston is not a big city so the cab back to your hotel won't be super expensive.
My favorite thing about Boston is the ability to walk everywhere. As long as you're in one of these areas, you'll be close to the action and within walking distance (20-40 minutes) to Fenway.
Check out The Verb Hotel It has rooms that look right at Fenway Park! I haven't stayed there but while looking for hotels, I saw this and thought it looked like the perfect place for people going to games at Fenway Park, and it has a fun music vibe going on!