You certainly don't need to go on the Strip to get a great meal in Vegas. One of the great things about Vegas is whatever kind of food you're in the mood for you can get and the quality will be very good.
Barrymore's is an excellent choice for high class food and to get an old-time Vegas feel. Far better food than the Peppermill and more low key.
Lotus is legitimately world class. But would need a reservation for dinner.