No problem with that.
I'd go to Shoreham in that case.
You can wonder round to Transair and have a browse in the shop. Alternatively, or as well, arrange to arrive around lunch time and make the very short walk along the road into the airport, cross the dual carriage way and take lunch at the Pad - you will get a really good lunch.
All within 10 minutes walk and there are always a few interesting aircraft at KA and a decent hard runway.
Bembridge would be better for the Spring or Summer. Lots of good trips out from the airport and even a stroll up too the beach (through the carvan park) gives some interest between the flying. There is really nothing at the airport. Forget the Crab and Lobster if you go there in the summer for lunch - it has gone down hill dreadfully in the hands of the new owners.
Goodwood is fine - the tea bar is OK and if you are lucky there will be a track day or some such in progress.
I know you are going mainly for the flying but even then its worth enjoy a short time at your destination.