Your vet is right. He is still very susceptible to picking up the diseases he's been vaccinated for.
However from a socialization standpoint... you still need to get him out. Do you know if there are a lot of parvo cases in your area? That's the biggest concern, some areas have a higher incidence of parvo, more loose dogs, what have you and in that case I'd be more cautious. In general though the risk of him picking up a disease is small, but the risk of him being cooped up and undersocialized is far greater. I definitely would not take him to dog parks or pet stores but a stroll around your neighborhood is probably fine.
Juno CGC: 3/31/09 "Reverse" Brindle, docked & floppy
Lucy: 2/1/06 Bichon/Poodle Mix
Happy: 1/2001, Rescued Border Collie Mix
RIP Molly, January 1997-April 8, 2009