I've eaten at the new Sandown clubhouse a couple of times recently, it's excellent.
At Bembridge, a reasonable lunch can be had at the Propeller Inn (edge of the airfield), but about a mile away is the Crab and Lobster, which does some of the best seafood in Britain imho.
Good workmanlike lunches at Popham, Compton Abbas and Old Sarum, but to be honest nothing spectacular (although in summer, the CA Ploughmans lunch, and the Popham salad buffet are both worth the trip).
If you like burgers, White Waltham does an excellent one.
G