I would recommend Red Rock Brewery for food. http://www.redrockbrewing.com/
If you like beer or spicy-ish food this a really good place. There is one in Downtown Salt Lake, and one in Park City. My roommate works at the one in Park City.
Park City is where they hold Sundance. Of course coming in March you will miss all the hoopla that is Sundance, but Park City is a lot of fun. Main Street is quaint and has interesting and odd shops as well as common stores. They also have the Alpine slides which are pretty fun.
Even if you aren't Mormon, I think temple square is worth checking out. But beware, the missionaries will try and talk to you if you are at temple square and look like you are from out of town or not mormon. They are nice, so it's not really that scary.
Gateway Shopping mall is fun to walk through but really it's very expensive to buy anything.
I agree that Trolley Square is interesting. Though it is undergoing construction it's still fun to walk around in.
As for nightlife (if you want to party with your mom :P) There is also Club Bliss. There are quite a few bars in downtown despite the main culture. Unfortunately if you go to a bar you need to buy a membership which is usually 5 dollars - it's because of Utah Alcohol Laws...very lame.
If you really like outdoors there are a MILLION hikes you can go on. Utah has absolutely beautiful scenery in the mountains. It'll still be cold up there, and there will still be some snow up there in March, but if you are outdoorsy, it might be worth checking out.
I hope that was helpful! And I hope you have fun checking out my hometown!