Street parking on Frankland Lane (just outside Crook Hall) is 40p per half hour. There's normally space here, but if not there is also Sidegate Car Park by the roundabout nearby which costs £1.80 for 2 hours then 80p an hour.
All fully paved paths along the river and through Durham, one steep set of steps up off of the river but otherwise fairly flat.
Though following the River Wear we didn't see anywhere that looked safe to access the river as it was too deep.
Plenty of bins along the river and through Durham
The walk starts next to Crook Hall and Gardens which is a National Trust site with dog friendly gardens and cafe, it's quite small but definitely worth a look round! The route then passes through the centre of Durham including going past the impressive cathedral.
We like this walk for when the weather isn't great as there's nowhere where it can get muddy! But it would be nice by the river any time. Although Durham is a very small city it can get busy, this route goes right through the centre but if it's busy and your dog isn't comfortable with crowds when you get to the Cathedral there's a path on the opposite side next to the Archaeology Museum which goes back to the riverside and cuts that part out without going back on yourself. We saw plenty of dogs off lead on the riverside section once away from the roads.