Plenty to do in Vegas for the non gambler, sightseeing, shows, outstanding restaurants, downtown at night, walking the strip or just watching the "goings on" center strip after dark, especially on the weekends. It should go without saying but stay in the high traffic areas, especially after dark. (They have more than their share of weirdo's)
From Vegas, the South Rim of the Grand Canyon is 3 to 4 hours away if you take the southern route, and 6 to 7 hours (IIRC) if you take the northern route (through Zion). You may want to consider staying in Flagstaff and going to the South Rim of the Grand Canyon from there (less than 100 miles)
My most memorable trip to the Grand Canyon was from Vegas up to Zion National Park and then on to the Grand Canyon. It's the long way around but really worth it IMO. Add some time for taking pictures when going through Zion.