Sexual activity is not the only way to pick up HIV. Skin is an effective barrier to transmission of the virus, but if you have a cut or abrasion and the bad luck to get some bodily fluid from an infected person on it you could receive a gift you don't want. There are a lot of viri out there, too. HIV is not the only one that would like to have you as a host.
No, I'm not afraid of contracting it just by visiting public places. I am, however, more careful about contact with people and objects than I once was. I don't go so far as emergency medical and law enforcement personnel, who now wear rubber gloves and face masks as a matter of routine, but I do what I can to avoid unnecessary risk.