Oyster Box - 10 minute taxi ride from Jersey Aero Club
Great seafood, great service and great beach-side location.
Bit of a long way from you.
With regard to Thruxton, easy to find, nice friendly people. Good facilities, interesting aeroplanes lurking if you know where to look.
'Restaurant' is OK for a builder's breakfast, plus reasonable coffee and cake.
Old Sarum café is a bit better and with a good view of the comings and goings.
SD