There are plenty of 21st century "geisha" clubs in Ginza. The mama-san will most likely wear a traditional kimono, but the women will be dressed very nicely in modern apparel.

You will need to make arrangements through a club member, and be prepared to drop ~ $2500-4000 USD/hr. for company + a rather steep price for every bottle opened by your party. And, you will open more than a few.

Forget about about dating or other arrangements with the women unless you're prepared to discuss your proposal with some ummm....colorful, generally large gentlemen in an alley behind the club.