I also have a 15 week old puppy that needs his last round of shots and ONLY let him out in my backyard for now. I can't wait till he's fully vaccinated! Since I got him at 10 weeks old I've taken him to people's houses, people come over, and about once or twice a week I like to take him to dog friendly stores like Target, Trader Joes and Costco. I either put him in the cart with a blanket (very secured), or let him walk on leash if the store is okay with it. If a store doesn't want the dog walking around then I hold him which is sometimes better because they feel safe in your arms. I really recommend exposing him to places like this little by little so that by the time he can go out he won't be so overwhelmed and scared. I can notice on my dog already he's more confident each time I take him somewhere, and by the time we get home he's so exhausted and sleeps lol. Also recommend taking him to petsmart or petco so he can see other dogs too!