The Hotel Monaco in SLC is nice and prices are generally really good.
In Park City there is a place called the Yarrow that most certainly will not break the bank. It is by no means a luxury situation, but it is a decent accomodation at a bargain price. There is also a Marriott in PC as well as condos for rent, or you could check out the Canyons Resort to see wha they might have. The Canyons is often a bit more pricey so may not be what you're looking for. If you want the ultimate budget buster hotel the Stein Erickson in Deer Valley is your place. Park City is a great town and I recommend staying there. There are tons of really great restaurants. Anything by Bill White is tip top.
in pc, you want to stay somewhere close to main street. you can walk to the bars and restaurants. if you don't have to stay in a hotel, i would check rental props at VRBO. there are some nice rental properties within walking distance to main street that are comparable or less expensive than the hotels.
with slc, it depends on what you want to do and that will determine where you want to stay. slc isn't a very big city. the mountains (little cottonwood and big cottonwood canyons) are only about 20-30 mins from dtown. dtown has a nice scene w/ a few bars and restaurants where you can walk around. if you want up by the mountains (what i recommend) then do a search up in little and big cottonwood canyon areas.
lots of things to do in slc and pc areas. there are GREAT inexpensive golf courses in slc. you can hike the mountains during summer. most of pc resorts have alpine slides, zip lines and stuff to do during summer. you can also mountain bike. there's a beautiful lake about 20 mins from pc. im sure they have boat rentals.
about an hour outside of pc is the strawberry reservoir. i've only driven through it but it's a beautiful huge natural area. they don't allow motorized boats on the reservoir but i've seen people in canoes. i would love to yak or canoe the reservoir.
i love slc. lots of things to do in the winter and summer. has cool bars and the peeps are nice.
I will also look into that park you mention. We'd like to stay near the mountains and also take in some sites in SLC. We wont be into the bar scene this go round.
Just search for places in Cottonwood Heights. Tons of condos around there along Wasatch Blvd. Easy access to Big and Little Cottonwood and not far from downtown SLC, either.
If you are willing to be a little further from PC/SLC, you could do Sundance. It is in/near Provo Canyon, which is a beautiful area. It has a great restaurant and bar onsite. Lots of outdoorsy things to do there in the summer. Great place to spend some time all around.