I've taken a guys-only March Madness trip to Vegas for several years in a row. It's a great time.
When we started you could get free cocktails for sports bets almost anywhere, but anymore....not so much. Most places want big (for us, anyway) bets for a single drink ticket, but since there are very few seats available unless you camp out all day anyway, it's easy enough to impersonate a slot player to get a cocktail and then head back to the book. A lot of places set up huge ad hoc sports books (Fremont, P-Ho, Orleans, to name a few) in ballrooms where they have big screens and drink specials. You can usually get a seat in there, especially for the later games.
Last time we were at the Hilton they still comped drinks, and the Imperial Palace will comp drinks all day in the race book, but not in the sports area. Sometimes we'll just sit at a bar playing video poker S-L-O-W-L-Y and watch the games on the bar TVs.
As far as cheap rooms, we like the IP. Can't beat the center strip location close to a lot of sports books and poker rooms with drunk tourists (like us).
Enjoy! And if you see a group of drunk middle-aged guys with Indiana/Purdue/Notre Dame shirts on, say hello!