If you want to stay on the strip the cheapest places will be Imperial Palace, Excalibur and Hooters. If you dont have a car I wouldnt stay off the strip, you'll just spend in taxi fees the amount you might save on a hotel room. I've stayed at Hooters before where they offer 12 free wings for every nights stay.
Hooters isn't really on the strip, plus, their wings would be better used as bath loofas than for eating.
Their address might not technically be Las Vegas Blvd but its probably 300 yards from strip and you can cut over the walkway and your there at MGM and NYNY. Won't disagree about the wings, especially in the casino.
The problem is that Hooters isn't right off the strip in the middle of the strip, like, say, the Westin is. It's off the strip at the butt end of the strip, which I should note is my favorite area of Las Vegas, but not everyone's.
I do most of my poker playing at Excalibur and blackjacking at Tropicana, if you're an old-schooler like me who likes looking rich but playing cheap then go for it.