It is walkable if you come out of the Acropolis site at the main entrance off of the Metro station side (the subway). (maybe a mile or so) But if you already have taken the Metro from the port into the city and have the all day train pass (or maybe even if you don't) you can go back into the subway and take the train to the Plaka station..You'll come out across the station from the tomb of the unknown solder, its a closer walk from there.. I'd have to look at the Subway map to give you the correct official names of the stations. You can find it online.
Ok.. I looked it up for you. If you come in from the port (Pireaus) on the green Metro line you need to transfer to the blue line and then to the red line to get to the Acropoli station This will dump you right at the main entrance to the Acropolis site. The point where you transfered from the blue to the red line is also the Syntagma station (Constitution Square) The Plaka area basically sits between these two stations so it is walkable form the Acropolis station. But the Syntagma is closer and if you get out there you can watch the changing of the guard at the tomb... But if you do we we did, you can see the acropolis and the other temples at the site and end up on the back entrance near the Thissio station (ask someone where the Metro station is or look for the M sign) then you can take the train over to the Syntagma stop to get to the plaka area.
DON'T get off at the Monastiraki stop. Yes its very close to the Acropolis but is is on the opposite side from the entrance and you will have to walk all the way around to get in (voice of experience here) We wasted a good 45 minutes doing this.
That is the bad news. We walked it but it was a long walk. Probably about a mile and a half. Our ship (Carnival Freedom) docked at the furthest point in the port from the train station.
I don't know if you could talk a taxi driver into taking you to the train station but if you could I would suggest that. Look at this map and the pictures before and after it. Our ship docked at the area marked "E12" the metro is just above that green square on the map. Its not hard to get to (just follow the edge of the port until you see the bridge in my picture) but it is a fairly long walk