I think it just depends on who is Minnie when you see her. Minnie is my favorite character too. I think it helps if you have one something that she can respond too like the shirts or shoes someone else mentioned. I happened to have a Mickey and Minnie shirt one and my Minnie ears. She was really sweet each and every time we saw her.
We saw her at Epcot character spot, and the Disney Visa. And at Animal kingdom in her safari outfit with Mickey. In the past she was at the character breakfast with Donald in Animal kingdom.
Try to do the character spot later in the day/evening. The line is smaller and so the characters take more time with you. Goofy danced with my DD and Mickey and Minnie were great.
I really preferred the M&G at DHS to EPCOT. Her room is just so much cuter at DHS, and it's more private. The interactions we had at both were excellent and she was in the same traditional outfit in each, so the environment gives DHS the edge. We only had to wait a few minutes for her after about 30 waiting for Sorceror Mickey outside her area.
One of our best character experiences period that happened to be with Minnie was at Animal Kingdom. It was later in the day during the afternoon, so the park was already slowing down. There was no wait to see her and Mickey. They made a huge fuss over our girls and spent a lot of time with us.