One more benefit to picking Spa, the Nurburgring is not that far away! Take your rental car for a spin (or rather a drive!) around the track
.
If you have any FF miles left over, also consider the run up to Montreal. There are lots of rooms and great restaurants in the city. The metro runs right to the track and for some reason the race always seems to have surprise. The Canadian fans are knowledgeable and they often have some entertaining support races.
Unfortunately the days are gone when you could walk up close to the pits. The last time I was there they did a pretty good job limiting access to ticket holders for that specific grandstand. Even on Friday and Saturday.
Have fun at Spa!