If you're staying close to Flamingo your best cheap burgers are going to be in the Koval/Paradise road casinos. They're not gourmet or anything - but big chunks of meat and cheap. Ellis Island will get you a 1/2 pounder in the $8-$9 range. Silver Sevens reportedly has a decent burger special too (I've not eaten there since it was Terribles).
In that same neighborhood is the fast food chain: Habit Burger Its comparable to In-N-Out Burger in quality and price...but they have more selection.
Shake Shack is a few blocks down the strip at NYNY. A burger, fries and shake will probably get you into the $14 range.