First time in Vegas?
You want to stay on the Strip; however, you want to go downtown one evening.
You don't want to stay at Circus-Circus, Riviera, Casino Royale and The Quad (and probably not at The Excalibur, either). If you want to stay at Caesar's, Planet Hollywood, Paris, Bally's, Flamingo or Harrah's, you want to check their prices directly in caesar's website USING CRHOME.
Unless you have plenty of time, you will not need a rental.