Born and raised Vegas girl.
Best places to eat are off the strip:
Nora's Italian on Flamingo and Jones. Make me jealous by having their melrose pasta. mmmm. Posh, not too expensive.
Soul2Soul on rainbow and Charleston.- Cajun pasta is amazing, and so is the crawfish bisque
Charleston and Ft. Apache- Kona grill. Everything is really good. and they have a great happy hour.
Hannah's is in the same shopping area (The FAB Boca park, my old 'hood), and try their house sushi or garlic noodles to experience heaven.
On the strip, go to the Paris Eiffel tower resteraunt if you have cash, because it is super expensive.
Shopping- stay away from all malls except the fashion show mall. Downtown in the Gaslight district, there are a few cute boutiques. Also boutiques in Boca park too.
The Belligio and the Wynn have beautiful gardens. Red rock etc has been mentioned. To be honest, I left vegas in part for lack of culture
. For your drive...how about the lovely Mount Charleston? 30 min. away, and beautiful at that time of year. It is just nature, nothing super exciting.
If you do go to the grand canyon, have a Navajo taco. Mmmmm....
Have fun!