I grew up in SLC and still have family there, so I go there once or twice a year. I have some websites for you, but I have to dig into my files.
First of all, Salt Lake is probably less than 50% Mormon now. You will feel comfortable there. Temple Square is the main Mormon tourist spot--definitely worth a visit, but be prepared, you will certainly be approached by missionaries. Smaller towns can be overwhelmingly Mormon.
You won't have a problem finding places that serve alcohol, although the Utah liquor laws can be confusing. You will find clubs and good restaurants. Shopping depends on what you are looking for. You will find all of the mall stuff. Eagle Gate is a new mall not far from downtown.
Park City has lots of fun shops, good bars and restaurants. I'm not a skier, so summer is my favorite time to visit the canyons and winter resort areas.
Sundance is fun to visit also.
Lots of great outdoor activity--hiking, boating, camping. I will go look through my files now, but if you let me know more specifically what you like, I can find out more for you.
One of my favorite places to take first-time visitors to SLC is Gilgal Gardens.
http://extras.sltrib.com/NIP/gilgal/index.htm
Both the Salt Lake Tribune and Salt Lake Magazine are good online resources.
http://www.saltlakemagazine.com/index.php?src=
http://www.slctravel.com/
Normally, the only real shopping I do in SLC is for books. Sam Weller's Zion bookstore carries a lot of books on the West, history, western authors, etc. They have a large used book section which I love to browse. http://www.samwellers.com/