I could probably write a short book in reply, but I will try to be concise.
Park City has over 400 miles of trail now. Most are suitable for XC/Trail bikes. The two most popular climbs up from PC are Armstrong and Jenni’s. Both of these end at Mid Mountain which is a 26+ mile “highway” of a trail. Almost every ride will touch MM at some point. You can go all the way up to the Wasatch Crest either from here. Armstrong-MM-Pinecone or Jenni-MM-Tommy 2 Step-3 Candle-Keystone-Shadow Lake - Blazing saddle - Puke hill will get you to the Crest. Then take that to Ridge Connector-MM-Hollys. Here is a route with the latter.
https://www.strava.com/activities/2551883285/embed/09ce09fe14675d166cbcff4e1f0ad76d582976c2
You can go up the DV side via Pipeline-Deercrest. Robs (between old PC and old Canyons) is another good way up.
You can also use paved bike paths to access Round Valley (via Rail Trail) or head over the Flying Dog (via Millenium Trail). Riding Flying Dog counter-clockwise is very fun.
The other big connector trail is the newish 9K trail which connects Empire Pass to the base of puke hill. Parts of this are pretty fun as well.
Avoid riding up Spiro or CMG. While allowed, it can be dangerous with the downhill biking traffic.
From MM near Deer Valley, you can take Tour de Suds or Team Big Bear up to Ontario Loop and Flagstaff loop out to Bowhunter. This isn’t a frequently used trail, but views are spectacular when the leaves are turning.
Let me know if you have any questions about specific trails or areas.