I assume that you mean that he's had his first set of shots, and you are waiting for his second series.
I would definitely take your puppy outside whenever you want, and enroll him in a puppy class. But I would limit his exposure to other dogs until he completes the full vaccination schedule. By that, I mean, don't allow him to have contact with other dogs' stools or saliva.
As you'll read in the links below, socialization at this age is extremely important. Particularly in the form of puppy classes.