OK, I'm a little late to this party, but thought I'd chime in. I am going solo for the first time ever...We've been 4 times in the past year with the kids and one other time where it was just me and DH. We have season passes this year and I wanted just ONE MORE TRIP!

So I am going alone. As for the dining...I often eat out alone (whether due to work or because I just need a break from the kids). I found you can do several things (most of which have been mentioned already). I usually have a paperback book with me...I've also had my iPod where I can 'people watch' while I'm eating. I don't have the dining plan, but have been there enough to know it's nice to sit and have a meal versus the rush rush of counter service. As for character meals, I am doing Garden Grill in Epcot when I go in a couple weeks. Not so much because of the characters, but because I think the food is really good there. And I was shocked because even though the trip is less than two weeks away (I just booked it yesterday), I got all the ADRs I wanted.
If you're nervous about having a meal on your own, I'd suggest trying it where you live first...like at your local Friday's or Chili's or something. You'll find the only one that might care about you being alone is you...
A funny story around that though...I went into Chili's once for lunch (during work) and the lady asked me how many. I said, "1"...She said, "Oh, I'm sorry". I looked at her and said, "Why? I'm not. I'm going to have a nice meal by myself and relax." I think I made her feel bad, but I thought it was important for her to know that eating alone isn't a curse!
Good luck to you!
Dawn McG