We saw Stitch a few weeks ago at Epcot, in the USA part. He came out periodically through out the day with the other characters there. You can ask a CM and they can tell you what times he is scheduled to come out.
I love Stitch too!! My husband tracked him down for me and we ambushed him at Magic Kingdom. All you have to is go to Guest Services when you arrive at the park. They will tell you when and where he will be making an appearance that day. Good luck!
Back in 2003 we got a photo with him at Lilo at MGM Studios...and in September....we rode Dumbo with him!! He was right next to us in line...got a great close up of him , DD14mths and DH!! He was right in front of us on the ride!!