You could say either "she works at a coffee shop" and "she works at a café." A dictionary might tell you that "cafe" is an accepted spelling; I prefer "café." "Coffee shop" is fairly common, particularly for places that are not very fancy.
Coffee shop is hardly used to designate a small café, if at all, in the Midwestern USA. Café with the accent would be considered showing off, but I admit that I like it better than cafe. In much fictional literature it is common to write that a woman works in a coffee shop and in regions of the USA a reader would immediately take it as a synonym for a small cafe. The modern, up-scale, places for drinking coffees exclusively are generally referred to by the trade name without mentioning coffee.
Both are right, but here in the US Midwest, coffee shops just have behind-the-counter servers these days. The word "waiter" tends to suggest someone who comes to your table and they don't do that here at coffee-shops anymore. I think they might have in former days and in very rural towns they might still do.
A café, on the other hand, does suggest that the customer is at a table and a waiter comes to it.
Oeco must be used to small coffee shops. We have several local coffee shops that have several baristas (or baristi, if you prefer, though most AE speakers seem to say 'baristas') and several waitstaff on hand all day. They also have dozens of tables and are very popular.
If it is a very trendy place that is active at night, it might be called a coffee bar, too. These became popular in the '90s, and we still have a local one that is very good and still quite popular.