Well, you got me thinkin'
First thing that came to my mind was dining. At sit-down restaurants, dining alone can be a little intimidating and boring. However, there are some dining options for a solo traveler that I recommend.
First, buffets, buffets, buffets. You don't have to sit and stare at the walls or ceiling waiting for your food - you just go up and help yourself.
Second, restaurants that provide some entertainment (of some sort or another). The Biergarten in Germany in Epcot (buffet, too!)
Teppanyaki Restaurant in Japan (watching the cook cook). Hoop-Dee-Doo at Fort Wilderness (good chicken, too). Sci-Fi Dine-in Theater, 50s Prime Time, etc.
Third, restaurants where you are seated with other people.

Well, maybe not THAT close. Teppanyaki (you are all seated around the grill), Biergarten, Hoop-Dee-Doo, etc. Good chance to strike up a conversation and meet new people.
I also usually prefer counter service because I don't have to wait too long for my food. I am not always a big fan of table service restaurants. Wait to be seated, wait to put in your drink order, wait for the drinks, wait to place your food order, wait to get your food, wait to get your bill, wait to get your credit card back, etc. A lot of waiting. Kind of gives "wait" staff a whole new meaning.
On another subject, I would suggest thinking about things you have always wanted to do, but have not had the chance because no one else you were traveling with want to do it. Nobody wanted to ride Dumbo with you? Go for it solo!
Go on some tours. Great way to learn cool stuff about WDW and also a way to meet new people.
When you are solo, you have more time to chat it up with cast members (and not have to be rushed by your party). Especially cool to do when cast member is not too occupied themselves. You can learn some cool stuff!
Try to set up a meet or two with some Disboard folks. I have done that before and it's fun! It's a chance to hang out with fellow Disney nuts.
Anyway, I hope this helps. Hope you have a great time!