Short answer: The Exeter Ship Canal towpath is the walk. It starts at the Quay, is flat for miles, and leads to two pubs out in the fields — the Double Locks and the Turf, which has no road to it at all. Riverside Valley Park is the shorter version of the same thing.
Exeter's ship canal is one of the oldest in the country and the towpath beside it runs south out of the city without a gradient worth mentioning. It is the best flat walk in this part of Devon and it starts at the Quay, which means you can do it without driving anywhere.
About an hour out along the water, through open country that feels a long way from a city centre you left twenty minutes ago. The pub sits by the lock with space outside.
Carry on and you reach the Turf, which sits where the canal meets the estuary. There is no road to it. You arrive on foot, by bike or by boat, and that is the whole character of the place. Check opening before committing to the walk out, because it is a long way back if the door is shut.
The shorter option, straight on from the Quay along the river. Open fields for dogs to run in, kingfishers if you are lucky and looking, and flat ground throughout. Good for an hour rather than an afternoon.
The towpath also gets you to Topsham, about an hour's walk from the Quay along the water. It is the best walk-and-pub combination near the city — and if you do not fancy walking back, Topsham has a station on the Exmouth branch line.
Dartmoor is the obvious ambition and the honest answer is that it is not a walk from Exeter — it is a drive or a sparse bus ride to the moor edge, and the good walking starts beyond where the buses stop. Canonteign Falls is the compromise at about twenty minutes out, with a flatter lower route as well as the climb.
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