We sailed Solstice on June15 ... 11-day Eastern Med. It wasn't necessarily the walking/climbing steps that was as difficult as the surface of the walkways. Many of these ruins have marble steps/walkways(eg. Ephesus). You want shoes/sandals built with good traction/rubber. Even running shoes are not always reliable (slippery surface).
And for those who wear bifocals, the unevenness/steps can be tricky through the lower half of your glasses. I found I had to look straight down very consistently. I had a lady my age (mid-50's)start this exact conversation with me on the way up to the Acropolis.
Brilliance of the Seas 2004
Costa Magica 2006
Celebrity Solstice 2009