One of the up and coming areas of Athens that has truly arrived also happens to be within walking distance of the Plaka. This is the area called Thission named after the ancient temple in the Agora that is actually a temple to Haephastus.
Thission used to be a place where few people went, especially tourists. Except for the temple you won't even see it mentioned in the guidebooks. But it is a fun neighborhood and there are some great tavernas.
To get to Thission the easiest way you would follow Dionissiou Areopagitou around the Acropolis and continue when it connects with Apostolou Pavlou street.If you are coming from the direction of Athinas street you can go to Monastiraki and walk up from the old Turkish Mosque at the square one block and take a right on Adrianou. Of course the easiest way is to take the Metro to Thission and cross back over the tracks and walk up with the Acropolis on your left when you leave the station. If you just walk straight down Ermou Street past Monastiraki square you will come to a small church called Agios Assomaton and a large square. If you turn left you will walk right into Thission. If you turn right you will walk into Psiri.