Park City has a great variety of accomodation for you to choose from. There is a page on
Park City Hotels that should help you find what you are looking for.
I would say the The Best Western Landmark Inn would be a good option. It is reasonably prices and has fantastic amenities. They also offer a Complimentary City shuttle through-out Park City from 8a.m. - 11 p.m.
Things to do would be skiing of course, Horse Drawn Sleigh rides, Tubing, Mountain Biking, Hiking, Golf, Scenic Air Tours, Horseback rides, Boating. Park City Main Street is fantastic for shopping with a mix of stores and a good choice of places to eat and drink. Also in the area you have a choice of museums and art galleries which you might be interested in.