The Isle of Wight only has two towns of any real size (and neither of them are exactly big!). Ryde has a population of 26,000 and Newport has one of 24,000. (All other IoW towns and villages have populations below 10,000).
Of the two, Ryde is probably the more tourist-orientated (because it's on the coast) and thus more likely to have hotels and restaurants open over the Christmas period. So that's where I'd start looking:
https://www.tripadvisor.co.uk/Hotels-g503890-Ryde_Isle_of_Wight_England-Hotels.html
The TripAdvisor reviews for the Lakeside Park Hotel seem to have several 5-star ones from people who've stayed there at Christmas, so it might well be worth considering:
http://www.lakesideparkhotel.com/