Ahh. Footwear and balance. Glad you brought up this topic.

I have the same problem with footwear affecting my vertigo.
I find barefoot is best.

I have tried all manner of different shoes, but find that the less between the bottom of my foot and the ground the more stable I feel. I know this might sound strange but even thick winter bed socks affect my balance if I wear them around the house. I haven't been able to wear my joggers for years. Heels are totally out - even really low ones.

What I do find is that the actual thickness and stiffness of the sole of the shoe is what affects me the most. I found some flexible espadrilles with a very thin sole made with a soft material upper. I can wear them without difficulty. I've also bought some non-slip stick-on pads for the soles because some of my "flip-flops" [as you call them in other places ], are troublesome because they are a bit slippery and I need to feel stable to walk anywhere.

[Strangely enough, I also have a major problem in the shower because the shower floor is moulded in one piece fiberglass and tends to flex under my feet and adds to my instability. ]

LOL @ Mark and his high heel comment.