Across the Peace Bridge on the Waterside, St Columb's Park is where locals walk. The riverside path runs alongside the Foyle with views back towards the city walls and the Guildhall visible on the opposite bank. It's peaceful in a way that the walled city, even at its quieter moments, rarely manages. Good for running, walking, or just sitting by the water while the city goes about itself.
The kind of quiet that a city gives you when you leave the centre. The park has formal gardens as well as the riverside path, and the full circuit takes about 40 minutes at a relaxed pace. Most visitors to Derry don't cross the Peace Bridge at all, which means this park is usually uncrowded. If you're spending more than one day in the city, it's worth the walk across.