Very highly ranked in my world list of good coffeeshops is Maroushia, the Fashion Internet Cafe (which is at least two-thirds correct, though I'm obviously not qualified to comment on the third). Located about three kilometers away from the harbor and the main tourist areas, Maroushia caters to the needs of a mostly-local crowd with an food, drink, Internet, and an almost-overwhelming sound system (of which I heartily approve, especially with the intro to the "I Love to See You Cry" video - wow, it jars my teeth). Two big-screen TVs play a ceaseless stream of MTV videos, even during the prime of World Cup mania, while guests sip their tea, play billiards, or surf the web with fashion and style. My particular habit was to commandeer the one table near an electrical outlet for hours at a time (usually three but sometimes six) and drink cup after cup of mediocre but reasonably cheap tea, often offset with a salad topped by with steamed crab or canned tuna.
One comment about MTV: either it changes its themes with frightening frequency, or it really is very different from place to place. The biggest difference is in the cut scenes: South African MTV has retro-anime/Lego-character cut scenes, Cyprus has some type of MAD theme (I don't know what it means), and Rome appears to have this annoying "de-De-DE-JAY TEE-VEE" announcement at all times. Most of the videos are the same, though the local videos so visibly pale to the glitz and glamour of American music studios they look like they were made with camcorders.
Incidentally, the pictured cafe is Maroushia I. Maroushia II is located nearer the tourist district (labeled as such, in English, on helpful street signs), and has a totally different vibe of which I do not approve. After a discussion on the merits of their approach with a new employee we decided that it was the best for that area, but it lacks much in comparison, especially when measured in decibels.