"I often go to a cafe."
"I've never been to a cafe."

Do these sound natural? Do you need to put "a" before "cafe"?

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"I've never been to a cafe." sounds perfectly natural, you need ''a'' because you're talking about any cafe. If you don't put ''a'' the sentence would have a different meaning, it's like saying that you've never been to a place named 'Cafe'.

An example so you see the difference:

''I never been to a city'' vs ''I've never been to London''.

You need the ''a'' when you talk about a generic noun.
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"I often go to a cafe." sounds fine but it depends on what you mean. In this case it sounds like you often go to one cafe in particular (but you're not saying its name for some reason).

Alternatively you can say ''I often go to cafes'' which means you go to a few different cafes, not just one of them in particular.