did my first solo trip this year also.
i never once felt funny or out of place, of course I strike up conversations with strangers at Disney all the time, so it was nothing new to me. and i really did enjoy meeting them.
i purposely did all the things that i can't do when i take the kids. i rode mission space, space mountain, test track, big thunder mountain, splash mountain, everything! what a treat!
i mostly ate counter service, but some table service. i even got into BOG for lunch. no problem, my iPad was my companion. sat and read, checked email,etc.
i agree with above posters, you can actually take time to look around you, relax and enjoy.....oh, and i actually got to SHOP! woo hoo
go and enjoy