At the pier in the Imax there's a family pub on the top floor with lovely views over the beach.
On the floor below is a Wacky Warehouse for LO to play, not for eating, with similar views if it's raining.
On the opposite side of the pier is the Oceanarium, also worth a visit if it's raining (or even if it's not). They have a nice cafe.
You could get the land train that goes along the prom to Boscombe Pier where there's a Brewster's pub with a big play area and caters for families. We went there after the Mile for Maude walk.
The gardens are lovely for a wander through and there's often something on like a band.
Harry Ramsdens is near the pier too.
There's an open top bus that you can get along the coast to Sandbanks and the Haven, and from there you can get a boat to Brownsea Island. Or in the opposite direction the bus goes to Hengistbury Head and there's a little train.
There's the beach, lots of facilities like deckchairs for the OAPs! Toilets nearby and drinks/icecream kiosks.
Will try to think of what else there is. There is tons!