I don't know if you already watched the anime だがしかし, that the story goes in a cheap sweets store in a countryside city in Japan. You know, I think this is maybe an awesome place to have a good time. So, for who knows, this is really a common place in Japan?
I have seen the show, but it's been a very long time :D
駄菓子屋 do exist, but they're way less common. I think it's thanks to convenience stores and supermarkets selling many of the same snacks, but don't quote me on that. Also the aging population and general urbanization.
Edit: I guess they're considered pretty レトロ at this point. I'm sure you could still find them though.