last week we spend a weekend on the Isle of Wight. We went from London to Lymington, then took the ferry to Yarmouth.
We checked into our AirBnb and then got on the local bus to Freshwater, from where we hiked towards the Needles Landmark, which is a rock formation in the sea not to far from the coast. During the second world war it's been used as a rocket testing facility and now been converted into a museum which can be visited during the day. Even if you don't come by the museum the view is definitely worth the walk.
The next day we took the bus to East Cowes from where we took the Ferry back to Southampton and the main land.