I have arranged the various places to stay in order of proximity to Beck Chapel where the ceremony is to take place. Please click on each logo to view the websites. I would recommend making hotel reservations as soon as possible, as there are frequently many events happening at Indiana University that can cause rooms to fill up quickly.

The Indiana Memorial Union is the closest to the chapel, and has the added benefit of door to door service from the airport to the hotel via the Bloomington Shuttle. In addition there are lots of things to do there inside - even bowling! Free wireless internet is also available.
The Grant Street Inn is a nice place if you want a cozy, homey feel. This bed and breakfast is a local favorite. That being said, the rooms are more pricey and as it is small, there is limited availability. In looking online the other day, there were already only a handful left.
The Hilton Garden Inn is newly built and conveniently located downtown. With 168 rooms, this is probably a good bet. The site describes amenities including complimentary high speed internet, microwave/fridge, and an indoor pool.
The Courtyard Marriott offers similar amenities. The Bloomington Shuttle also offers door to door service from the airport to the hotel. (I am not sure about the Hilton, but I am sure that they offer some mode of transportation there as well.)
The Scholars Inn is a restored 115-year-old mansion that has six suites, and offers the luxury of a gourmet breakfast in bed. Again, I have a feeling that availability will be limited.
In the unlikely event that you are unable to make reservations at any of these locations, click here for these and additional listings in order of proximity.