Durham is a city steeped with history and the peninsula walk is a pleasant circular walk along the banks of the River Wear.
The walk is mainly along good riverbank paths (suitable for pushchairs), however there are three sets of steps to climb / descend which may cause difficulty for a heavy pram.
There are lots of things to see on this walk including rowers, ducks, waterfalls, a weir, a unicyclist (well there was one the day we did the walk, so you may be lucky), not to mention of course the castle and cathedral high up in the centre of the peninsula. If you are a visitor to the city, it is definitely worth taking the extra time to explore the heart of the peninsula as well. The views from the top of the cathedral are quite spectacular (and will show you the route of your walk).