Looking to do the same with mine, I have been on a few track days with my brother who is a massive petrol head.
I would reccommend (if you don't mind a little bit of travel) Bedford Aerodrome, they do regular track days at reasonable prices. Also you can do an evening session (which is great now the clocks have gone back), the benefit of these being that they are slightly cheaper and last for three hours, which is plenty of time for a first outing.
I have been to this track a number of times in my brothers cars, and the atmosphere is great, very friendly and open staff and the track is great too. With a mix of technical courners and great straights to boot the Z on!
Check out this link for the track:
http://www.clubmsv.com/car-home/calendar.aspx?venID=Bedford&duration=&gclid=CJTQhtqem68CFcEPfAodHQ_jdw
Good luck! I'd also be interested in a Z4 owners track day...perhaps if you get enough interest we could get something sorted out....