You can certainly walk really comfortable with Nike Air Max sneakers. I'm not sure if I would wear them as running shoes. I think they're not really meant for that. Nike apparently agreed and now has released the Nike Air Max 2015 ID.
These shoes are perfect for running. The sneakers are also perfect for running on hard grounds, like streets. As of yesterday it's possible to make your own version of these sneakers here. It's available from € 235,-. Not cheap, but running shoes are often expensive.