Guess this answer is better late than never!
I've been solo for the CP for two years now. Last year I ate at the Biergarten. That is fun solo because you sit at a table with other people. Last year the table was filled with others going to the same show of CP so we had something in common to start with. This year I decided to live dangerously and tried Restaurant Marrakesh for the first time. I had a blast!!! The food was wonderful, there was music and the belly dancer to watch and the servers were wonderful. I didn't for a moment feel awkward about being solo.
I highly recommend NOT bringing something to read when you do a sit-down at Disney. I used to "hide" behind my magazine or book and Disney was the place where I learned to not do that. There is so much to watch, so many people to "peek" in on. Disney has taught me to value the moment and experience I am in, instead of tuning out what is going on around me. It took very little time to get comfortable with so much to see!