Shelly's Barbershop, Pinkie's Pan-Fry, and Mary's Merchandise. Wheels can only be bought in grey buildings. The three establishments mentioned are the only grey buildings more than six spaces away from any subway and, therefore, relatively safe from para-Vamps.
Watch out, though. If a gang owns a nearby Joint, even these safehouses may not be secluded enough! For example, if a Vamp's gang owns the Palace Chophouse, she can reach Shelly's Barbershop via the subway!
Vamps especially like to target opposing Racketeers in grey buildings because those buildings have only a single entrance such that vamped Racketeers cannot easily get revenge on their next move (by moving to declare a hit on the Vamp). In addition, in the advanced game, vamping in a grey building offers the opportunity to become a Siren on the next move!
Notice that in the question I said that no mob had Wheels yet. If a vamp has Wheels, NO building is vamp-proof! Then it is best for Wheel-less mobs to keep their Thug close to their Racketeer to forestall Thug-vamping.