Besides walking, here are some driving tips from Plaka, in order to plan your trip to Athens and other close destinations.
Piraeus port: without traffic jam 15-20 minutes, with about 40 minutes
Athens Airport: without traffic jam 45 minutes, with more than one hour
KTEL- Bus departures & arrivals across Greece (there are two stations, one at Kifissos, second at Liosion): without traffic jam 25 minutes, with about 40 minutes to both ways.
National Railway station (OSE) 40 minutes max.
Lycabettus hill: 10 minutes
Parnitha: one hour to the sidehills, it depends on how you want to reach the top, not more than two hours in total
Penteli: one hour
Ymmitos & Moni Kaisarianis: 40 minutes
Tourkovounia hill: 40 minutes
Beletsi Lake: one hour
Sounio: one hour
Lavrio: one hour
Rafina: one hour
Saronikos: to Piraeus and then by ship to Aegina etc: 2-3 hours
Salamina: 50 minutes to Perama port and then 25 minutes by boat
Olympic Stadium: 45 minutes
Marathon: one hour
Elefsina: one hour
Olympia: max 4 hours
Delfi: max 4 hours
Thiva: one hour and a half