A CTC survey showed York to be the safest place to cycle in Britain, and just a few minutes in the town will demonstrate that it’s much less stressful than London. There’s a courtesy in car/bike interactions that doesn’t exist in many other cities. But that’s not to say it’s all easy.
The one-way system around Fishergate and Fawcett Street, aka the ‘Fishergate Gyratory’, is a notorious junction. New crossing improvements have eased the situation a little, but we’d still suggest finding an alternative route if possible. South of here, Fulford Road (the A19) is busy and difficult, despite on-road cycle lanes, and you may prefer to travel a little further to use the riverside path.
On the opposite side of town, Bootham Bar (west of the Minster) may be picturesque but also has a poor safety record, with cars regularly running the red lights.
You’ll need to keep your wits around you either side of the railway station – that is, from Queen Street, over Lendal Bridge, up to Museum Street. The narrow road is invariably full of traffic, not least buses turning and pulling out.