Just because I've been there and done it doesn't mean that you can. You know your limitations, I don't, so if you go there it is at your own risk. By mentioning the place I'm not suggesting that you go there.
Durlston Country Park, Lighthouse Rd, Swanage, Dorset, BH19 2J
Durlston Country Park and National Nature Reserve was a great place to visit using an off-road mobility scooter, but the roughness of some of the cliff-top footpath means that it was probably advisable, even though I have my own, to use their off-road mobility scooter, a Tramper, provided by the charity Countryside Mobility. Next time I'll probably use my own but avoid the worst section (which is only a short one, and easily avoided). I was glad that I'd phoned ahead to book a Tramper as one of the two was being repaired. I was very surprised, given the distance and gradient of the hill, to see a manual wheelchair being heaved by a young helper from the lighthouse, but that really was pushing it!
The main footpaths at Durlston hug the coastline, offering wonderful views over the sea wall, even from a seated position, as does the long path to the lighthouse, both were well worth doing. There was also a decent cafe, and a disabled-friendly toilet.
The footpath down to the lighthouse at Durlston Country Park.
The lighthouse and holiday cottages at Durlston Country Park.