Hi - while staying at Son Pac we walked over to Arenal. (Don't try walking it in the heat of the day, like we did!) Arenal had a lovely beach and lots of bars/shops/restaurants. I remember it as being very hilly, so quite a steep climb to get around.
If you fancy a day out, try a walk (or bus) over to Son Pac where you can have a game of golf. It's a lovely golf course and you can hire almost everything that you need. If you don't want to play golf you can still walk along the course where there is seating areas. Take lots of bread, as there is a pond at the far end, with lots of ducks. The children will love the peacocks that have 'right of way' and wander all over the course. If you carry on walking straight, past the pond, you take a walk through a nature reserve - more of a rough track through trees, but a short cut to the spar shop and the beach - quite a walk to the beach but worth it as the beach at Son Parc is lovely, very shallow for the children. Not a lot else there apart from 'The Strip', which consists of a small row of shops/bars/restaurants. There is a restaurant at the Golf course open to everyone and not just for those playing golf.
Going further along the coast you come to Fornells. (Too far to walk to) No beach there to speak of but they do have boat trips round the harbour which the children might like. Lots of boats and some water sports. It's a very flat walk at Fornells but we thought that the restaurants were very expensive.
On that side of the Island the bus (as far as I remember) goes to and from Mahon to Arenal, Son Parc and the Fornells area but if you want to visit anywhere else you really do need a car. Otherwise you will have to take a bus into Mahon and then get a bus out again. If you do venture out take the children to Son Bou. There is a maze there that my grandchildren (ages 5 - 8 - 12) loved and it kept them amused for ages.
Have a great holiday.