On this subject, I used always to eat out alone before an evening play or show, but the attitude of others eventually wore me down. And even at the theatre itself I might as well be a member of an endangered species. Where are all the other women who visit the theatre alone? (I deliberately don't say "single women" as I'm not one; my partner just attends very rarely.) There don't even seem to be that many men who go alone, but I feel (and obviously this is just my perception) that they are ignored or accepted whereas I am regarded as an object of curiosity or pity.
Come on....just brave it out! I do regularly! I have found everywhere quite open to single dinners and just take a play to read when I am not eating! I do find the service can be a bit quick so my meal tends to proceed quite quickly! Just smile and enjoy yourself and remember that no-one rally cares what you are doing...they are all too busy being concerned about their own lives!