In a word Filton welcomes GA, there is only 1 training organisation there to my knowledge in the form of Aeros, and alot of privately owned GA aircraft there, (EDITED to say, sorry Coanda, just read that you posted this 🙂 ) they fit you in really well, I had a flight today and when I returned they were extremely busy but accommodated me really well as ever, they get alot of ILS approaches there from training aircraft so it can get busy sometimes but nothing too great.
There isn’t too much at Filton to look at, obviously Concorde is there, there is no restaurant or cafe as such but a very short taxi ride will see you in Filton itself and there are a few cafes etc there, it is even walking distance if you have a spare 20 minutes, visiting aircraft get the privilage of parking on apron 1 which is by the ops building, us residents have to use apron 2 which is the other side of the airport and have to drive, if you arrive and they tell you to park in apron 2 tell them to shove off as you can’t walk to the ops office :). Landing fees I “think” are about 15 pounds.