Depending where on the campus you’re going, there are several sensible routes between York city centre and the University. But by far the most pleasant is along the riverside, crossing at the Millennium Bridge if you started on the west bank; then continuing past the barracks, and over the Walmgate meadows, to the campus. It’s largely traffic-free or very quiet; you’ll only meet significant traffic at the light-controlled Fulford Road crossing.
The River Ouse path provides an easy, largely traffic-free, cross-town route. A dedicated cycle path starts at Skelton and crosses the meadows, meeting the east bank of the river at Clifton. You’ll need to manhandle your bike over the narrow Scarborough Bridge to cross to the west bank. There’s no riverside path in the very centre (south of Lendal Bridge), but you can cycle along Skeldergate until rejoining the river.
The route finally swings away from the river after the new Millennium Bridge, where you can swap banks again for Fulford, or continue south towards the railway path and Bishopthorpe.
The easiest route from the east of the city to the centre is the Foss Islands railway path. This starts from Osbaldwick and Tang Hall, with a new bridge over the River Foss to link it to the Minster. It’s direct and fairly fast, though the stop-start path through the retail park is exasperating. Watch out for broken glass.
Crossing the city centre isn’t straightforward. You can head for Bootham and then south to Scarborough Bridge, which avoids the busy central bridges. From there, a cycle path skirts the station before reaching the quieter paths and roads of the western suburbs.