Not really. You can enjoy time alone if you like. Usually people like to socialize with other people, regardless of where they are - including at a cafe. But that doesn't mean you can't be alone at a cafe. As long as you are enjoying yourself, I don't see how it's weird. If people find it weird, then that's their business. But you're not likely to see them again anyways. And even if you do, who gives a shit? They've never walked a foot in your shoes, so they don't understand you. Stand your ground against other people's perceptions of you.
No, just bring a Book and take a Look... At all of the People. No big Deal. I was in McDonald's alone Yesterday while Waiting for my Roomie to Pick me up for dinner. I enjoyed my Sundae and Time alone, going through all of my bags of things I had shopped for, and Watching the News. People were Talking to me. No One, hun, ever Really cares what You are Doing, it's None of their Business. Good luck. xx