Went to East fleet a few times (thanks to OH's unemployment haven't been away at all these last couple of years, so the last time we went was a good couple of years ago).
Here are some suggestions, and depends on the age of the parties (and the weather)
Abbotsury swannery - very good, and takes Tesco vouchers
The Nothe fort - highly underrated. You can expect to spend hours here, and a lot of it is indoors
Crab fishing on weymouth harbour walls - use fish from the fish and chip shops rather than buy bait
walking/cycling on the disused rail/tram tracks on Portland or in the New Forest
walking to the top of the lighthouse at Portland Bill
If you're so inclined (and have a bit of cash) take sailing lessons at the Laser centre in Portland harbour Osprey Quay (would need to book in advance)
the New Forest is only an hour or so away - you could book a pony trek (again, somehting to do in advance and a bit pricy)
Enjoy your holiday
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