There's a disabled parking area at Watersmeet, which you can get to off the A39 on a narrow lane with sharp bends - there's also a drop to one side towards the end. The numbers for permission (National Trust) are 01598 752648 or 753348.
An alternative might be to park at Hillsford Bridge (there is an NT car park there, through some stone gateposts). Watersmeet is about half a mile away along the river and there is a gradient (the height difference is about 250ft), but it's a good path and there are no steps or very steep sections.
The Pavilion in Lynmouth is nice as Toopaz says, and it has good views across the coast. An alternative which is leafy and rural is the Lee Abbey tea room, on the toll road beyond the Valley of the Rocks, which has a small car park very close by. (It's beyond the abbey itself, in a cottage-style building).