Outside of sleeping, we spend very little time in the room.
It has always been nice to stay at ther team's hotel. In past years, there have been many activities planned for the fans at the team hotel such as pregame parties, postgame receptions, send-off celebrations, etc. The past couple years, these parties have been at the hotel nearest to the Savvis/Scottrade Center.
The hotel rates can vary widely in St Louis, and also depend on other activities that are going on in town that weekend. Last year, many Bradley fans were unable to get into the Renaissance Grand because of a large convention that was going on at the Edward Jones Dome (something to do with quilting and crafts). Most years, there have been plenty of avilable rooms at Bradley's hotel. But if you are interested in staying where Bradley and many of the fan stay, it would be best to book early, as soon as we know what hotel that would be.
If booking at the lowest cost is important, then it may be better to wait until a couple months before the tournament when hotels usually start discounting their extra rooms.