>>172361As an add-on, there is an observatory nearby at Butser and if you are into Urbex, an old quarry (before you get to QE2 from Petersfield direction).
Also look at the INTECH Centre in Winchester. Good star-stuff there every so often.
Chatted to Dad and camping up the top of Butser itself may be easier, there's a car park and other bits I'm sure you can find a way.