I've never had a problem, and I usually dine alone. There have been times when I was unhappy with the selected table, and I just politely state how the selection doesn't suit me (either too close or too far away from the action, as suits my mood) and the people have always been very gracious. You have to wait a bit more, of course, and they can treat you like you're going to explode at any minute sometimes, but I think they try to do the best that they can given their own situation and priorities. I've found that being patient, polite, firm, and best of all, clear, is what works best.
If you WANT to be seated away from the noise, or if you WANT to be left undisturbed by the characters, then DO mention your needs when you check in, and again to the waiter/waitress when they first arrive.
I agree with the other poster who mentioned that the characters will tend to short-change a solo diner or a party of all adults. This is understandable, since their job is primarily to entertain the kiddies. If you want interaction with them, then you must make the first step. Tell a joke, compliment their outfit, whatever... they will follow your lead.