I agree with mookie that you should try and stay downtown. You don't need to stay at a high end place but there are plenty of hotels in Boston close to MBTA lines. There are also hotels close by in Cambridge or Brookline. You don't need to stay within a mile of the Garden, The TD Garden is literally above the North Station stop on the T.
Boston is a very walkable city, plus getting a taxi to and from the arena if you are staying somewhere in the city is also an easy idea. Parking is very expensive so unless you have any specific plans to travel/sightsee outside the city, you don't need one. So, that's one savings.
Flying in on Thursday shouldn't be an issue. The first semi final is at 5 so depending on when your flight would get in, you need to plan for getting to whatever hotel you're staying at, and then getting to the Garden.
Mind you, it's a regular work day so any traveling around the city will happen during the afternoon commute.
If you want to start researching and need to know where a certain hotel is located, etc, just post. Between myself, mookie and even les, we should be able to help!