The Courtyard Boise Downtown is within walking (and viewing) distance from campus and the Taco Bell arena. The RAM Brewery is right across the street from the hotel. It's not in the heart of downtown, but close.
If you want to stay in the heart of downtown, I would also recommend the Grove Hotel. It's within walking distance of EVERYTHING downtown and within walking distance from campus. It would be a longer walk to Taco Bell Arena from the Grove than the Courtyard, but still doable.
If it were me, I'd stay at the Grove Hotel. If you don't want to walk to campus, you can catch a cab for pretty cheap.