My Vet said my puppy should not go anywhere until his last shots? What are your thoughts?

The current and long-standing position statement of the American Veterinary Society of Animal Behavior can be viewed here:

AVSAB Position Statement On Puppy Socialization

Another good article on the subject can be read here:

Socializing Your Puppy: Why “Later” Is Too Late

We get our puppies OUT!! My two cents is your puppy is not 100% safe ANYWHERE. One thing is pretty for sure… and your vet may not have told you this part… if you don’t get your puppy out and about before 16 weeks old (ish) then you have missed the socialization boat completely.

I believe how and when you do this is a very personal choice, but a choice you should have ALL the information on before making it.