We like Park Resorts at Shanklin (Lower Hyde) off season (although we'll have to go in the school summer holidays if we go again and I'm really not sure about that!)
It's got a lovely little indoor swimming pool (as well as an outdoor one, but I'm not that brave in the UK), a playground, and the campsite is on level ground away from the statics (and I think they've had a new toilet block since we went). It's a short walk from the shops at Shanklin (in particular a Somerfields supermarket) and the Dr's (dd2 had extremely bad nappy rash last time we were there and we ended up seeing a Dr!). The beach is probably too far to walk, but there's a little sand train or you can park down on the road next to the beach. I think there's a soft play centre on the seafront too. Newport (the main town) is only a short drive, and there's the usual range of shops (including an ELC which can while away an hour or so if it's raining!) There's also a big cinema in Newport.
We like Shanklin, but we're thinking about trying Ryde next time we go - Ryde is a different character to Shanklin or Sandown, Ryde has a long flat seafront with boating lakes, fair and a swimming pool etc, where as Shanklin and Sandown are more cliffy, with the towns on top of the cliffs and the beaches below.
It's a lovely place to go, it's got all the home comforts you need (like familiar supermarkets (Sainsbury's, Tesco, Somerfield, Morrisons etc) for particular nappies etc!) but feels like you're going abroad as you go on the ferry!
Red Funnel do a special offer where you can go for so many nights out of school hols and book an all inclusive package with campsite and ferry.
Let me know if you want to know anything else, hope I've not confused you too much!