There are so many amazing "fine dining" establishments in Vegas, I wouldn't know where to begin. I don't think I've ever been disappointed by the food there in a half dozen trips. I'm sure some people will have useful recommendation in this realm, however.
When it comes to fast food, I recommend In-N-Out Burger (there are numerous locations throughout the city, and one very near the strip [
link]). It's a classic west coast burger joint specializing in fresh, simple, inexpensive burgers_fries_shakes. The fries seem to be a love-em/hate-em proposition ... I'm not a fan, myself. Everything else makes up for it, though, IMO.
The Dean Martin Dr. location I linked to above also has a museum beside the restaurant. It's interesting enough to warrant a brief gander.