Basel Restaurant

Walliser Kanne in the city centre is supposed to be the best Fondue in town (though not the cheapest!).
Website: http://www.walliserkanne-basel.ch/en/welcome.shtml

Fondue is a dish from the Alps, it is not a local dish in Basel. It is also winter food, only tourists eat it in summer.

Be aware that Switzerland is very expensive, Basel included. I spent quite a lot at low-level pizza near Fondation Beyeler some years ago.

There are many Italian restaurants in Basel, due to the many immigrants. They are the cheapest "sit down" food in Basel. A pizza will cost ~CHF 15, depending on which one. Plus any starter (salad, soup), plus drinks.
The Walliser Kanne will cost three times this.

My favorite affordable place to eat in Swiss cities, including Basel, is Manora. It's a high-end cafeteria on the top floor of the Manor department store. The food is not left sitting on steam tables; for instance, if you order fish, they take a piece of raw fish off the ice, cook it, and hand it to you. For 3 CHF you can add beilage to a main dish, meaning all the starches and veggies you can fit on the plate. Delicious, and half the price of a regular restaurant with servers.

The only catches are that they are always mobbed (Swiss people know what a good deal they are), and they are only open department store hours, which in Basel means 8:30 to 20:00 on Monday to Friday, 8:00 to 18:00 on Saturday, and closed on Sunday. And a lesson I learned the hard way: they stop serving an hour before they close! Since the food is prepared fresh in small batches, when they stop making it, it doesn't linger. I got there at 19:15 one night, to find that only desserts were still available for purchase.

Manora won't have fondue, but if you're looking for a cheaper but still tasty alternative to Swiss restaurants, and want a sit down place instead of getting food from the supermarket, they're great.