The new admin email should appear in the whois in a max of 12 to 24 hours. You should also recive all confirmation requests there to. I also recomenc you change your registrar to www.eNom.comwww.Joker.com or Star_Gate - cheeper and much easier to handle.
First off, paying GeoCities for their hosting is not silly at all, especially for people with just a couple of domains/websites who are looking for some user-friendly interface.
Registering a domain name through them is a bit on the expensive side now that the average market price is below US$10, but you may always transfer registrar next year.
Closing an existing account too soon is definitely the newbie experience you need to learn, but hey, who hasn't been a newbie?
But many domain registrants still don't understand the rule of NEVER to use an e-mail of the very same domain you are registering as the Admin Contact; since if there is any problem with your host, it will only make modifying your DNS info more difficult.
Last but not least: it is not impossible to recover your domain even when your Admin Contact e-mail is not active. Most registrars have the mechanism for legitimate owner/registrant to do so by e.g. sending them a fax and/or with copies of say your photo ID and things llike that. You might want to check out their FAQ for this.
Hope this helps.
Co-Founder@HostHideout. Profoundly influenced by #Bauhaus, @Nameslave unrepentantly embraces #Minimalism with a bias for functionality, color theory and pixel precision: a #multimedia messenger in the McLuhan sense. His totally irrelevant M.Ed. dissertation examines Organizational Culture and Change Management. He also likes Patrik Ervell, Wong Kar-wai and IKEA.