Elvis is a souvlaki shop. If you have tasted souvlaki already it's probably not like Elvis'. The whole shop is Elvis themed and the staff is super relaxed and friendly. They don't serve souvlaki with pita like most of the restarants, but just souvlaki with fresh fried potatoes, lemon and bread.
While staying in Athens you will probably go out in Kerameikos sometime. There are a lot of cool places around Elvis and the only place open late at night is this shop. It's the thing you need after drinking, and the square right outside is the ideal spot to enjoy your souvlaki.
Between chicken and pork, i would definitely suggest the pork souvlaki!