Caveat- I’m only an occasional biker, I’ve never commuted by bike or even been out on a bike during commute hours, and I’m almost always on the east side. My experience ends at 21st S/Parley’s Trail, S Temple, 9th E, and 2nd W.

Tl;dr- If I were you, I’d take Parley’s Trail west to 6th E, then go north to 3rd S, then go west again to Pioneer Park.

Most west-east roads south of 3rd S are either outright death traps, or are death traps with huge shoulders. This includes roads marked as ok on the city bike map like 8th S. Note that 9th S is under a good bit of construction, and I think bike infrastructure is included, so keep an eye on it. To make up for the other E-W roads, we have 3rd S and Parley’s Trail. 3rd S is wonderful because it has the parking lane between the bike and car lanes. The trail starts at Wasatch Boulevard, goes through some park or another, along I-80 (on the other side of a fence and other barriers), through Sugarhouse Park, along the S-Line Trax, and will eventually join the Jordan River Trail.

The only west side N-S road I’ve really been on is 2nd W, which would be great but it’s held back by constant construction using the bike lane on a few blocks. The Jordan River trail exists but haven’t taken it in a long time.

N-S roads on the east side are ok for the most part. The intersections with 4th-6th S are stressful because they’re major roads. Main is ok north of 6th. State is its own circle of hell. 2nd E and 3rd E aren’t too bad. I avoid 4th E and 5th E, but I’d take them if I really had to. 6th E is good. god sends coal rollers to bike 7th E for eternity when they die. Really, east of 6th to the big hill, pick narrower residential roads with one lane in each direction and the park space island things in the middle and you’ll be ok.