Well, if you want to visit SLC, your best bet is the KOA in town. Convenient to downtown (Temple Square, restaurants, museums, etc.) and also to both I-15 and I-215, so it's easy to get anywhere in the area.
If you like more rustic accommodations, check out some of the Utah state parks. You may need reservations for popular times (weekends, holidays).
Be aware that the week surrounding July 24 is a busy time in Utah, and lodging rates will be higher than the rest of the year. Pioneer Day is a Big Deal in Utah! :)
Within a day's drive north or south of SLC you will find some wonderful national parks - in case you have never been to Yellowstone, Grand Tetons, Bryce, Zion, Arches, etc. You may want to look into some of these (it will be hot the farther south you go, of course.)