Sharper, only reserved seats are usually on the race book side. Bunch of old timers there reading their papers and smoking pipes. Have seen some reserved spots at Cantor books, prob have to have some juice though. Also, Cantor's books burn out my retinas. Monte Carlo's book is very small. I watched a UFC card there once and was not that impressed.
Like BIGDAY said, Bellagio is huge and nice, get there early or you will be sitting in the library like seats with the dividers. Nice thing about Bellagio is free drink service, as long as you have a betting slip, although it takes forever when it's packed. Atmosphere gets pretty nuts during big games. I did Green Valley Ranch last year for March Madness. Was great, dollar beers and hot dogs and plenty of great seating. Really nice, clean book and it's mainly locals who are pretty laid back.
If I had to recommend books on the strip: (Drink service is important on my list)
LVH
Mirage (Drink Tickets)
Bellagio
Aria (Drink Tickets)
Wynn (Drink Tickets)
Any Cantor Book
Off Strip: Green Valley Ranch
Some people have said Lagasse's Stadium is the shiz...every time I've walked by there has been a line out the door. Seems like more hassle than it's worth to drink and watch a game.
Also, if you're looking for good bar food in the Monte Carlo, check out "The Pub." Big ass burgers, tons of beer. Not a bad spot to watch a game either in a pinch.
I will be there for the Madness...not sure which weekend yet though.