We’re scheduled to arrive in SLC about 3pm on Saturday, July 11. We want to spend our first night somewhere in the mountains between the airport and Moab. We’ll be in a rental car and would also like to pick up some supplies that evening or the next morning. We currently have reservations at the Holiday Inn Express in Heber City. Is that a good choice or would someplace in Park City or Provo be better? My boyfriend specifically wants to see/drive through the Wasatch Mountains. Any suggestions would be much appreciated!

Park City or Heber City would be a 40-mile detour, but they're in the Wasatch mountains.

I don't know what supplies you'd be wanting to buy, but I think you'd find everything you'd need right in Moab.

Stop at a grocery store in Green River UT so that you won't be paying the tourist prices in Moab. When we went to see Arches and a couple other parks, we stayed for a week at the Robbers Roost motel in Green River and saved quite a lot of money.
Maybe plan out the route to see the Wasach on the way back to SLC from Moab starting out early in the morning.

If you really want to hit the backroads, go for it. You could up to Heber (around 40-60 minutes from SLC) to stay the night and then the next morning go down canyon to Provo. That's just a short blip and is totally out of your way. It's 4 hours from SLC to Moab. Halfway point is Price--not scenic at all, good leg stretcher for young kids is the Museum there. Heber City is really nice and less expensive that Park City. What supplies do you need? Camping/etc? You can get that at the REI in SLC on the way to Heber. If you are talking groceries--good grocery stores in Moab. If you need a Whole Foods or Trader Joes, then stop in SLC. The whole foods in Park City is really nice, too.