We live in the area (probably passed you in the beach 
)
I would definitely recommend the IOW for a day out. We sometimes leave the car in the car park at Southsea, get an all-inclusive ticket for the hovercraft/train/steamtrain and have a lovely old fashioned day out. out.
The hovercraft is a fun way to cross the Solent and you land by the train station. You catch the train to a station in the middle of nowhere (the station staff will know) and that is where you can catch the steam train. It's all rather good old fashioned fun.
The Spinnaker tower is a good day out and so is the Portsmouth dockyard, which are just round the corner from each other. You can see the Warrior and the Victory, (although the Mary Rose is not on view at the moment, sadly). As I recall, the entry price to the dockyard includes a harbour trip, which my DS enjoyed more than anything.
The Southsea part of Portsmouth also has a sea life centre and a lovely flat harbour walk, perfect for pushchairs and bikes.
Chichester is nice, too. Have you tried the Walls Walk? It's fairly easy going and takes about an hour or so to navigate the city.
Petworth isn't too far either - it's NT and very pretty. We often go there at the weekends.
The Weald and Downland Open Air museum is quite near and that's a lovely day out, too. Ducks, a mill, houses to explore and fab walks -what more do you need?
Or you could park down at Itchenor and walk along the harbour path. That's a welly walk though at the moment but you could lure the family on with promises of seals basking when it's quiet...
Or park at the marina and walk around there - it's flat and mostly paved, plus you get to see the boats using the loch to get in and out. My DS is fascinated by it. And part of the walk takes you past the end of the canal, where you can see swans and ducks. We were getting up close and personal with the fluffy little cygnets and ducklings yesterday.
HTH (we love it here as you can probably tell!)