When Miles was a puppy, I took him EVERYWHERE with me. Literally, everywhere. In fact, I think a lot of the reason he has such a good demeanor around all sorts of people, kids, and other dogs is because I exposed him to so much. So I think you're doing a great thing! That being said...
I successfully took him on trips through Target, Walmart, Cheeseburger in Paradise (on the patio), Walgreens, even Nordstrom (just a quick trip in and out!). The great majority of people loved having him there and would ask to pet and hold him.
We only had a problem once, and that was at Walmart. There was a Taco Bell inside the Walmart, therefore it was against certain codes to have animals inside. The funny part about this is that when the manager stopped me, he told me I would have to take Miles outside "unless he was a seeing-eye-dog". I almost rolled on the floor laughing. Did he honestly think this 2-lb yorkie puppy in the front of my cart sleeping was guiding me through the store? Anyway, I gave him a friendly argument that Miles was cleaner and better behaved than most toddlers (no screaming or poopy diapers), but it didn't matter.
Now that Miles is grown up, he doesn't go too many place with me, but we still go into Walgreens occassionally. He'll sit with me in the pharmacy while waiting for prescriptions, or browse the store while waiting for photos. We've been to Walgreens a million times, and they've never said anything. We get complimented all the time on how well-behaved and relaxed he is. It's like he's seen it all so many times before, that it's no big deal to him.
I think the moral of the story is...if there's food preparation/groceries involved, you could be asked to leave. Some restaurants are pet-friendly on the patio (I used to work at one, and we didn't mind dogs at all). Good luck!