i guess it all depends what you are interested in.
we love history so have focussed on things around that.
there is the museum of menorca in mahon which is interesting and all the exhibits have english explanations. the harbour boat tour is good. there is an art gallery on the island in the harbour with a little cafe. we haven't yet done the old military hospital tour but plan to. there is also the xeorigieur gin factory walking distance from mahon centre (lots of free samples!).
there is a direct bus from punta prima that is very cheap.
ciutidella is beautiful and lovely just to wander round and have a relaxed lunch but is a bit more awkward to get go on public transport.
if you check online there are fiestas over the summer which are a great experience for immersing in the local culture.
we also like to visit a traditional menorcan bakery and pick up some local bits. they are dotted all around mahon.
punta prima itself is quiet but enough to fill an evening for a wander and variety of food. the beach can get busy during the day. there is a nice walk heading right away from the beach along the cliffs. there is a small playground for little children behind the main road.
the road train is fun for kids and we tend to take it to binibeca and have a meal at Bambu (booking essential!)
that's as much as we have done but there is still more to explore. i just love how low rise and relaxed the place is.
i can have a look at which online supermarket i used (one was much easier than the other) if you want to do that? there are the usual shops in punta prima but can be pricey and fresh choices variable. if you are hiring a car there is a l