You can use the Monastiraki subway station as the Psiri area is right next to the Monastiraki area. Go to the Anargyron street, which is right in the middle of the action.
You can see the greek youth in crowds walking up and down in the former poor and industrialized part of Athens center. The place is full of contradictions. There are some inexpensive cafeterias which serve beer, wine and ouzo until very late at night which attract the more bohemian part of greek youth. There are also some very stylish clubs, bars and cafeterias which attract the more trendy and fashionable part of greek youth. There are also expensive restaurants with live music which attract older crowds. All these people are crowded in the small and old pavements of Psiri among an industrialized environment of the past decades. It is worth visiting if someone wants to see how greeks spend their nights out and is right next to Monastiraki so it can be included in a walk in the Athens center.
There are a lot of restaurants with live music but bear in mind that they can be quite expensive. Even the restaurants without live music can be expensive so check the prices before you enter a restaurant in Psiri, especially if it looks very stylish and trendy.
Avalon, Leokoriou 20 (at corner with Sarri street) - Psiri, tel. +30 210 3310572. Open until 01:30.
Pairs Keròs, Taki 16 (on Psiri square). Tel: +30 210 3212858. Refining "mezedopolio" with live music every evening. Open also on lunch hours.
Orea Penteli, on Psiri square, tel. +30 2103218627. Another "mezedopolio" with live music in an old restored building.
Skolion, Katsikogianni 5. On Agii Anargiri square -- Psiri, tel. +30 210 3246098. A "mezedopolio" where local singers sings rempetika music.
There are many great clubs such as ENVY, Candy Bar, Saloon Oriental, Venti, Fetish, Luv, Liosporos and many smaller ones.