Depending on Dubs' feelings on the subject, I have a cheap spray bottle that can make a pretty fine mist, and I spray Aoife down with it whenever she's too dry and it's hot, pretty much. Chest/belly/underside is the best for cooling, and then anywhere that his fur is short. This doesn't work as well when it's humid, but as long as the water is cold, it has some benefit. A dip in the tub works even better, if the dog doesn't mind and your cold water is still running pretty cool.
Ice packs can be an options if Dubs will tolerate them--when it's really hot here, you can sometimes find the humans and the dogs draped in ice packs for a few minutes at a time, then they're returned to the freezer to try again a little later.
Definitely open windows at night and close them first thing in the morning if you can, although I find that works better the first day or two of a heatwave, and then the building seems to heat up and stay warmer.
For activity/exercise, I also second water play! Get out the hose, the sprinklers, the kiddie pool, something like that, and have some fun that way. Keeps them from going stir-crazy, but doesn't encourage them to overheat so much like walking or playing without the water might.
The car (with you in it at all times, for safety's sake) is a good option in some cases, and much calmer than all the various stores you mentioned. It isn't the greatest for the environment or your gas bill, so I'd only do it in urgent circumstances, but I've definitely sat with my dogs in my (running) car with the air conditioner on while reading a book or eating or something.
I've never lived somewhere with an air conditioner in my life--the weather where I currently live (and was raised) doesn't usually require it, but every year we get some days over 95 degrees and no one has a/c, so we've got tricks for those days. When I was in grad school, I lived where it was over 90 degrees every day from May through October, and about half the time over 100 degrees. We had no a/c then, either--of course Casey and I were both a lot younger then, but we managed!