Rapunzel - Get to MK for rope drop and make the dash for the 9:15 show (the first one of the day). We did this and we were the 3rd from the END of the line. I've heard stories of people who went to join the line at 9:45 or so and had to wait for the 12 pm (not sure on the exact time) show.
Tiana - Liberty Square, in the gazebo behind the Christmas shop. She has set meeting times and I'd suggest getting there 30 minutes prior so that you can join the line. We arrived at the exact start time of one group and we were turned away (this was the first week of May), so I just sat in the shade, took a break and waited for the next start time.
Ariel - I think she can be found in Adventureland, but I'm not sure since we were able to skip this princess (we saw her at CRT, so DD was satisfied).
HTH!