I think many of you will know that I take a lot of holidays alone - not just out of necessity but because not many women of my age want to do the kind of things I do on holiday, like snorkeling on coral, white water rafting, or tramping for miles up isolated mountains. (Juragran is an exception, of course, and a perfect holiday companion, with a very understanding husband!)
I have no qualms about going into pubs/restaurants/cafes alone either, but I don't go to the cinema because I, too, am rather claustrophobic and I would need to sit on the end of a row very near an emergency exit! Oddly enough, the one situation in which I am trapped for up to 13 hours in a confined space - flying - does not bother me at all.
I think it is better not to think that other people are looking at you and thinking you are a 'Billy no mates'. Most people are not even interested in why you are on your own anyway. Anyway, who cares what strangers think? I wouldn't let it stop me doing anything I want.