Hi Craig,
Don't want too much then?
Camping Het Amsterdamse Bos (Amsterdam Woods) is in Amstelveen woods about 2 miles from a motorway exit. Under 30 minutes from the city centre by public transport - I think they run a transfer bus from inside the camp - some facilities on site, but like most city centre sites the pitches can be on the small side.
Camping Zeeburg is also about 30 minutes from the city centre - on a small island to the east of Amsterdam - probably not as convenient to access the centre of Amsterdam.
I prefer the sites a bit further out in the Dunes - Duincamping - and then catch the train or use the P+R
I'm in my Rotterdam office Monday 19 to Wednesday 21 - if you have anything specific I can try to find out for you
Robert