Are you going to have a car? If not, a plan on spending a lot on cabs or taking the bus. I recommend Rincon de Buenios Aires and Viva Mercados. Most, if not all, of the "non-tourist" restaurants are off the Strip.
A Vegas rookie, huh? I am sure you will hear the name Rosemary's very often! It is a great place quite a ways off the strip though. Lotus of Siam is a Thai lovers dream. Those are my favorite off strip places.