Nothing is more fun then having a new puppy and wanting to take them everywhere with you. Puppies go through a key socialization period up until around 16 weeks of age. During this critical time (and even after), it is important to socialize your puppy the right way.
Overwhelming your puppy: quality vs. quantity
You don't want to overwhelm your puppy and you want to make sure you always stay in control of the environment because after all, you are your puppy's advocate. Going to a big box store during prime hours can easily overwhelm your puppy. Choose places that expose your puppy but you won't have to worry about them being overwhelmed by families, children or too much stimuli all at once.
Puppy food and treats
Always take your dog's food and treats with you when going to new places.
It's a good idea to never let strange dogs approach your puppy (or vice versa), or to never let people approach your puppy without your permission. For fearful dogs, we can accidentally teach them to be more fearful if we don't advocate for them.
Strangers and Puppies
If you want to let a person approach your puppy, give them a treat and have them give it to your puppy. Thank them, then move on. If your dog is fearful and doesn't take the treat, just have them toss it on the ground and walk on. Forcing a dog to interact with someone will only make them more fearful.
Dog Parks and daycares
Dog parks should be avoided only because they can harbor disease and because it's an uncontrolled environment. Taking your puppy to a good daycare, or puppy classes once or twice a week is a good substitute for the dog park.