If you are going out west, one thing you will have to factor in is the driving distances. They are huge! A buddy of mine wanted to "swing by" Mt. Rushmore on a business trip to Helena, MT a couple of years ago until I informed him it was at least a 12-hour drive...one way!
I think your decisions will revolve around what you want to do for the vacation. As you see above, none of the National Parks are really day trips from the SLC area.
If you want to tour parks specifically, I can give you some suggestions, but none of them will involve SLC.
1. Fly to Jackson, WY for Jackson itself, Grand Teton, and Yellowstone. Jackson is one of those really cool western towns, and if you immerse yourself in Teton and Yellowstone for 3-5 days each, you'll come away with an incredible experience. At Yellowstone, get Old Faithful out of the way early in the morning and spend the rest of the time in the backcountry. If you walk 1/4 mile down virtually any trail, you'll be alone.
2. Fly to Vegas for Death Valley, Zion, Cedar Breaks, Bryce and the Grand Canyon. If you go to Grand Canyon in the summer, go to the North Rim, not the South Rim. I'd overnight in Vegas, Zion, Bryce, and a rim-view cabin at North Rim. I've done that as a quick 4-5 day trip, or it can be done as a 7-10 day relaxing trip.
3. Fly to Phoenix -- north to Montezuma's Castle, Sedona, the South Rim, east to Meteor Crater, Petrified Forest, Painted Desert, north to Canyon de Chelley, Mesa Verde, and then SW to Monument Valley (whew!). We did that trip in a week, but it was a blur.
If I wanted quality rather than just touching bases, I'd probably fly into somewhere in CO (Montrose, maybe?) and just hit Mesa Verde -- it's one of the most beautiful and interesting parks in the entire almost-400-unit park system.
As we all know, there's nothing like staying onsite. In national parks, that's even more true than WDW because of the remoteness of most parks...and the quality of the theming.

Unfortunately, we don't have an NPS-VC, and there's no NPS dining plan.
That said, most parks have a variety of lodging ranging from backpacking to very luxurious. Some of the best accommodations are rather simple -- but they're clean and comfortable, and there are many budget options. Some of the best meals I've ever had have been in lodge restaurants after a long day on the trails. And champagne is really deadly at altitude...
If I can help you with anything in the parks, please let me know. The website is
www.nps.gov and you'll find a park-finder thingee on the home page. Key links to look at in each park are "Planning your visit," "In Depth" and "For Kids."
If you have kids, don't forget to check out the Jr. Ranger program in each park.