How old are your children (if you have them)? Difficult to suggest without knowing but here's some ideas....
Osborne house - seaside home of queen victoria, good day out, there is a cute little cottage she built for her children in the grounds too.
Butterfly world - indoor greenhouse with butterfly's, actually the butterfly's fly more when it's sunny but it's indoors.
Dinosaur isle museum
Quay arts centre Newport - gallery exhibition place and cafe
St Catherine's light house
Amazon world zoo
Dimbola lodge - photography etc, home of early photographer Julia Margaret Cameron. Dressing up in Victorian clothes room, shop, tea room
Rosemary vineyard - indoor bit showing you how they make the wine, tasting included. Recon children would like to see how everything's made too.
Yarmouth is a good little town for a mooch round on a wet day. Quaint streets and shops.
If the weather brightens up best beaches are steephill cove and Compton bay, if you like to go somewhere less touristy.