When we were preparing for our trip to Portugal this year, my husband became aware of Lisbon's infamous/famous tiles and read about making sure to wear grippy shoes. We went shoe shopping for that reason and also because we did need new shoes. We both ended up picking pairs of Vans shoes (these ones were called deluxe because the insole was extra padded) as it seems to be grippy.
Imagine our surprise when we got to Lisbon and observed that Vans (and other similar athletic shoes like New Balance) are super popular there, not only among young people but also people who look middle age. Also very popular in Porto.
Anyhow, I guess for anyone who wonders what shoe to wear, you might want to try Vans. It feels like Vans is even more popular in Lisbon and Porto than any major city I've visited in the US!