Re: Athens
I'm not the typical traveller, so I can't add much to what athanaric said apart that you should be visiting Monastiraki square and its surroundings by evening time and eat some food locally. I also advice you to move to the seaside (both Phaliro or Glyphada) and look around for fish restaurants, as the Greeks are the best when it comes to octopus and squids and can produce awesome fish food.
There are some areas in the center (Athinas road) that one would probably avoid, but all in all I have been there many times and NEVER had any real trouble.