As a UK resident both of these seem crazy to me - on our little island we find any distance a chore! 😂
if you’d like a suggestion, I would recommend either hiring a car or getting a taxi and going to Lymington (or if you hire a car you could just explore the South coast, which is beautiful).
Lymington is a lovely Georgian town with an active sailing scene, loads of fabulous places to eat and a very pretty nature reserve walk.
However, if you’d like a recommendation between the two, I would also go for Windsor for exactly the reasons given by BklynBorn47. It’s an extremely pretty town and quintessentially English. The late Queen’s favourite home 🥺and home to Eton Collage. 😊