The Pi Pizzeria is just off the U of U campus and is really good. The John Browning museum is a few minutes north in Ogden at Union Station along with a train museum and a small car collection IIRC.
Union Station | Ogden, Utah
The Pie Pizzeria - People's Choice for Utah's Best Pizza for over 30 years!
Temple Square is interesting regardless of your religious beliefs. The central downtown area is all within walking distance of there, and has lots of shops etc. It's been a few years since I have been there, and I left when I was 19 so I don't know the nightlife, but as I remember you have to buy a "membership" as there are no bars only "private clubs." It essentially amounts to a cover. You also can't order a double, you have to order a single and a side car. I don't believe you can purchase more than one drink per person at one time.
I lived there for about six years through the end of junior high and high school. It's a nice enough place, lots of great outdoors things to do. Wages are lousy, it's really tough to make a decent living as an employee and the cost of living isn't lower than many other places. That's one big reason I never went back. My mother finally left there to move to Washington state. She was an RN making $21.00 and hour at the state psych hospital. Her wages doubled as soon as she moved here!