If you’re still in Shef, have you made it out to the peaks yet? I highly recommend the route out to Damflask reservoir via Penistone road, Hillsborough then loxley road. The bit in Sheffield isn’t particularly nice of course, and there’s a short section of tram tracks. But penistone road has cycle lane for most of it. The climb out of town may or not be hard depending on fitness... but isn’t super long so you can always hop off and walk. The road to damflask does get some twats, but isn’t too bad. There are loads of cyclists from beginners to full Lycra types that use it, so I think regular drivers are pretty used to cyclists.
Once you get to damflask the views are already nice, and there are flattish and fairly quiet routes around the reservoir. You can also use it as a jumping off point for more advanced routes if they take your fancy.
For easy riding the route from near the law courts along the Don to Meadowhall (or indeed all the way to Rotherham) is ok. Though there’s a bit in attercliffe where you have to go along some industrial roads (not too busy). But it is the only entirely flat route you’ll find!
There’s a decent routing app called Komoot you can get. The first section of map is free, and will get you Sheffield and the peaks.