What would you call a shop like a coffee shop, only without so much coffee?

I’m thinking about opening a coffee shop in a couple of years.
After asking this question a couple of days ago, I realized: “coffee shop” isn’t even the right name for it. I thought I had finally nailed down a conventional name for my ideas, but then I remembered something. I don’t like coffee. I love the atmosphere in coffee shops, though. So I need to figure out a name for it. This shop I’m hoping to open will have cookies, muffins, ice cream, and coffee. Maybe some sandwiches/wraps. So what would you call it? Not a coffee shop or a restaurant…. I’m also hoping to cater to a younger crowd (teens) – they’ll be able to do homework, sit & read, maybe use an empty room for tutoring after school.