Most of the campsites have some sort of bar/party tent which goes on until silly o'clock in the morning.
Camping F1 on Winterhills is right next to the volunteers' campsite so very close to gate 5 at Copse, however they made us proper grumbly last year as they went on until after midnight on the Saturday and we had to be up to collect radios at 0545 on Sunday!
Have a look at
Hamilton Fields, around a 20-30 minute walk to the circuit (just outside the village to the east). They have a fairly strict noise policy due to their proximity to the neighbours.
Silverstone Woodlands (the official site) has segregated areas for 'lively' tents and families. Expensive it may be in comparison to some but as I understand it the facilities are good, it's well managed, and it's very close to the circuit behind Stowe/Vale/Club.
Whittlebury Hall (Park) is also very close. Some guests of mine have popped from the volunteers' site to the bar/marquee there a few times and it seems to be very good.
There are more up around the village, and some slightly further afield but those are the ones of which I have second-hand knowledge.
Wherever you end up I'm sure you'll all have a hell of a time
