I can see the IP of everyone who accesses the site - its a built-in feature of vbulletin.
Various ways you can get an IP, direct connection is easiest. Knowing what city someone is in doesn't help much, unless you have their name which you can cross reference with local information from their area, or an email address which you can tie to their online identity elsewhere which is often revealing. With an IP if you want to file police charges you can file a police report and get the police to subpoena the ISP for their info, which provides their real identity and address, and the ability for court injunctions/charges.
Cookies don't do anything to prevent any of this.
Someone having your IP address doesn't matter much. It matters much more what other information you make available about yourself online.