The place I would be recommending because of its price and location is closed now, The Imperial Palace. Sure, its not top notch, but its location centre strip is excellent and I'd much rather have a 24 hour burger bar and Hash House Agogo over all the fancy designer shops of the posh ones.
I stayed at the Bellagio too, and found that kind of wasted on me, the room was the same, perhaps smaller than the IP and it's a significant walk from your room to anywhere else on the strip (walkways etc).
One thing, for sure, its don't fall into the Brit trap: booking Circus Circus or Stratosphere, which are miles away and total dives ("I've heard people say 'but its cheap', yes it was (for a week), it was 1 quid less than staying in Imperial Palace, and 5 quid less than staying in the Flamingo or Harrahs.
Personally I'd recommend against staying down the south end: MGM, New York New York, Excaliber, Mandelay Bay, Tropicana or Luxor. Its not midstrip, its one far end. The centre allows you walk down that way, or go the other way up to the rest of the hotels...