I wouldn't go to a character meal by myself. I would feel SUPER strange about that.
Despite the advice that's given here a lot, I wouldn't eat at the bar as a solo. I think I would feel more pressure to be social with the people around me or the bartender, whereas at a table I'm comfortable just people-watching.
You know, I sometimes open a "solo traveller" thread even though I've never been one because I wonder if you'll post, and it reminds me of the time we ate together at Biergarten in 2009. Hope all is well with you!! (and we'll have to meet at the Biergarten again soon!)
I will not eat at a table service restaurant during a solo trip. I have eaten many solo meals on business trips and other occasions, and have read about other solo travelers' positive experiences about dining alone at WDW, but I can't bring myself to do it. I realize that its completely irrational, and want to encourage other solo diners to continue to do it and share their stories. Hopefully one day (soon) I will get over my phobia!