Missing busy main roads completely is difficult but they’re not too bad away from rush hour and loops can be put together mostly avoiding them.
From the Uni, I’d be heading west over the Dukes Pass (Callander via Doune) and back via Aberfoyle. Or add a few miles on by taking in Loch Katrine (closed road, and stunning!)
Or – head out to Kippen, Fintry, Carron Valley and back into Stirling.
Or – head east through the Hillfoots, across Glen Devon and back via Auchterarder.
These routes can get icey is the temp drops and can be done keeping off main roads.
I work on Uni campus and there are a couple of roadies there that will be happy to give you more info. Ping me an email if you want me to pass your email address on.