The Island has a lot to see and do, but would take more than one day.
There is Osborne House and grounds, the tour around the house takes about an hour or so then there is the grounds which are extensive, as well as Swiss Cottage.
Carisbrooke Castle is another couple of hours or so to visit, it held King Charles 1st prior to his execution.
Havenstreet Railway is another good place to go, and if time permits a ride on a steam train.
Then there is the Needles and Alum Bay (think Coloured Sands) and the pleasure park and glass studio.
Ventnor Botanical Gardens are another nice place to visit. They have a sub tropical microclimate in that location s a different variety of plants and flowers normally found.
That's just a few places, but with travel will take time to get to, and with Island roads as they are, longer than a similar distance on the mainland.
Like most tourist areas it depends when you are thinking of coming over.