I did a search through the archives, but I'd love more suggestions.
We have all hardwood floors, and my 2.5 yo is obsessed with wearing slippers in the house. We have a pair from Target that look like thick socks with a nubby slip-resistant bottom. The problem is that the lining doesn't stay put, so we're constantly having to pull them up and fix them. Whatever we get needs to stay on his feet and also help him not slip on the hardwood floor as he runs through the house at top speed. I don't mind paying for quality if I don't have to buy them every 3 months.