If you're into funky-old homes and neighborhoods, Sugarhouse area is very popular among younger people. It is not entirely flat, but not into the foothills yet either. There is good public transportation near downtown, near the University of Utah (but that's hilly), near Sugarhouse, and in various other places. I live on one of the foothill benches in Sandy near Little Cottonwood Canyon. My rides are always hilly; no matter which direction I go I'm buying a 700 to 3500 foot elevation gain by the time I make it home again.

Have a look at https://www.rideuta.com/ and consider locations with good bus and light rail access. From my home to the Historic Sandy light rail station it's about four miles down a hill. I can get there in under fifteen minutes. Coming home takes me a half hour on bike. Once I get to the light rail, I can get downtown in 25 minutes. You probably want to be closer to downtown, and closer to the rail.

Also, Salt Lake and Utah Valley have an extensive MUP system that can get you from Ogden all the way to Provo (If you're inclined to ride 200 miles each way). The main artery is known as the Jordan River Parkway, but it has offshoots here and there to take you into other parts of the city as well. I've taken it from 90th northbound to about 45th, and I've taken it southbound all the way to Saratoga Springs (from my front doorstep that's about 60 miles round trip). The MUP is mostly flat with a few exceptions near where the Salt Lake valley and Utah valley meet up. It's not in the most convenient location -- at least for me it means I have to pass under the I-15 freeway to get to it. But once on it, you can put on some distance pretty quickly. Here's a map of the MUP and bike lane system: Salt Lake City / Salt Lake County Bike Map

Salt Lake City and the surrounding municipalities have reasonably good bike lanes, though sometimes I'm frustrated by a first class lane suddenly ending on a busy road with no shoulder. I suppose that happens everywhere you have cities that were developed before bike advocacy. But SLC is one of the better places in the country for bike advocacy and accommodations.

Salt Lake City's best riding is the foothills and canyons. Riding Wasatch is great: You can get from Draper to Midvale with only about eight traffic lights, covering 20 miles. And the view is very nice, as it overlooks the city. Be prepared for some hills on that ride though. And heading up any of the five largest canyons on Salt Lake's east side gets you into some beautiful countryside, at the price of about a pound of sweat and tears.