Standing on top of the Acropolis, looking at the Parthenon and surrounding areas is certainly worth the cost of the plane ticket that got you there. And its looming presence is visible from almost every where in city central. If you've extra time in Athens, a second visit is worth the 2000 drachmas admission fee. Filopappos Hill is also a great location for keeping vidual over this historical monument around the clock during down time.
Even with Athens hosting the 2004 Games, Olympic Fever is part of the daily diet here. Olympia, home of the first Olympics, is a long bus/train ride away but Athens hosted the first "official" Olympics in 1896 at the white marbled Panathenaic Stadium...a modernized version of Hadrian's original for Gladiator contest during his 76-138 A.D. reign. Several additional Olympic stadiums and compounds are scattered around the city.
Nestled below the Acropolis, the pedestrianized areas of Plaka and Monastiraki are definitely worth indepth exploring where newer shops and restaurants blend quite well with 2000+-year old ruins and everything else from in between. Considering your limited options, there'll be no need to hurry!
Quick Tips:
In 1900, there were only a few thousand inhabitants in Athens. One-hundred years later, 3-million+!!! Civil engineering and development DID NOT keep up with the population growth. Be prepared for traffic congestion, air/land pollution that's pretty disgusting.
Athens/Greece in general yielded the only "culture shock" I've experienced in Europe. Things are still pretty primitive - for example: Plumbing is old; toilet paper can't be flushed but must be placed in trash receptacles by sides of stools. Even in some of the fancier places, cans hadn't been emptied nearly often enough!
This is a trip you'll definitely need to do your homework before leaving so you know what you're experiencing. In almost every site/attraction, information is given ONLY in Greek. Street markers are both Greek/Anglo alphabets, bus signs/routes were only in Greek. Unless you're proficient in local language, consider this mode of transportation obsolete.
In 3/99, I averaged 300 drachmas on the dollar, but they didn't go very far. (i.e. large cup of coffee 450 drachmas!) Overall, it's not as expensive as northern Europe but still there weren't a lot of good deals for budget travelers as inflation was high.
Best Way To Get Around:
Walking...and a lot of it is by far the easiest, sanest way for getting around Athens.
Avoid having to drive ANYWHERE in the Athens metropolitan area. Cheap cabs can also run up quite the hefty fares sitting endlessly in congested traffic.
Athens, like Rome, is in desperate need of Metro expansion, except every time they start digging they hit another potential archeological excavation site. The most important line/stop you catch is Monastiraki for going to Piraues. Cost was 45-cents. Remember to validate your ticket before boarding as officers were checking.
Peloponnisou & Larissis are side-by-side train stations in NE central Athens where you can travel to various parts of the country on slow, rattle-trap commuter lines that's just like being part of something from an old Greek movie. A one-way 2-hour ride to Corinth was .15.
Transportation tickets ARE NOT sold round-trip. For ferries going to islands, different reps sell tickets dockside at suprisingly reasonable one-way rates. However, be prepared to pay 25%+ more for your return ticket once they've got you stuck out there!
Other transportation-related info/tips regarding flights, ferries are covered in my ADDITIONAL TIPS entry.