Where you're visiting in February, your personal interests make a big difference in what you might find interesting to do here. Probably the most obvious question: Do you ski or snowboard? If you do either, you need to go to Snowbird/Alta and Park City. If you do not do winter sports at all, then you will still want to go to Park City for the restaurants and to experience the overall vibe-- it's about a 30-minute drive from Salt Lake City into the mountains. Make sure you get specifically into Old Town Park City.
In Salt Lake City itself, since you've never been here, you need to be aware that Utah has a unique culture heavily influenced by the fact it was originally settled by the Mormons. I'm not LDS (Mormon), but I would encourage anybody visiting for the first time to visit Temple Square, which is in the heart of downtown. The site is owned and operated by the LDS church, so much of what is taught from an historical perspective is biased in that direction, and there is a pretty overt religious message directed at visitors as well. You'll either be touched or caught up in morbid fascination at the unapologetic nature of the whole thing. Completely non-threatening, though, and well worth the visit.
Due mainly to Utah's liquor laws and strong bent toward maintaining a "family-friendly" environment, we're a little bit backward in terms of what folks in other cities consider "nightlife". You can certainly find dancing/clubs, but nothing I would personally waste my time on as an out-of-town visitor. We-- finally-- are getting some really great restaurants in town (see Dr. Jones' thread in this forum about his condo rental for recommendations), and you will find some good local brews, if that's your thing. Again, we have some ultra-conservative liquor laws here, so the actual percentage of alcohol in adult beverages is lower than elsewhere, but that doesn't necessarily mean bad booze.
Going to a couple of Jazz games is going to be the best part of your trip. If your wife is interested in other sports at all, the Grizzlies are the local semi-pro hockey team, and their games are always entertaining. There are several venues around the city-- mostly in the downtown area and within walking distance of Vivint Smart Homes Arena (that just rolls off the tongue, doesn't it?) that have a pretty steady slate of quality musical talent. You may want to look at tickets for these performances in advance, since there are some truly great bands/solo acts. There are a couple of comedy clubs in town that are so-so, but probably not worth your time unless you're a huge comedy fan. You might enjoy either Keys on Main or The Tavernacle, which are bars featuring live dueling piano entertainment-- surprisingly fun, almost always packed with an upbeat crowd.
There are tons of other things to do, if you dig around. I'm not sure of your budget or interests, but if you're here for an extended time I would recommend finding a couple of daytime excursions that take you out of the city up into the mountains-- snowshoeing, snowmobiling, that sort of thing. Utah is, ultimately, a destination spot for people who love the outdoors, and a lot of money is dumped into creating a world-class experience for that target group. Anything you can do to at least visit the ski resorts and see what they're all about is time well spent.
Hope that's helpful, and I have to say-- you're a lucky man to have a wife who is essentially taking one for the team so you can watch a couple of Jazz games in-person! haha... Where are your seats?
