You don't say when you will be renting the car....
It is a difference between winter, when it gets dark at 5 pm and summer when daylight lasts till 8 pm...

You should calculate about 4 - 4 1/2 hours for that trip.
You will follow the highway from the airport to Tripolis and Sparti, then further to Gythio and Monemvasia.

Streets are in good shape, and usually there is not much traffic after Sparti.

Once arrived in Monemvasia and in case that you have booked a hotel within the castle, it can be very possible, that you will have to park the car far away from the gate to the old city, and you will have to walk carrying your luggage.
Very often there are too many cars parked on the street, so you will have to leave your car far away from the gate.

Also do arrange to be picked up at the gate by the hotel, many hotels are offering this service, if they know when you will be arriving ( a short phone call before you arrive in Monemvasia will make things easier). Some hotels are far away from the gate and the main street and dragging a suitcase may not be very easy, depending on your physical condition

Driving back is very easy, just follow the sigh to the airport, take the exit to Kifisias Street and drive towards centre, it is a very long street that will take you straight to the Panathenaic Stadion. Ather the stadion you will turn to the right and at the end of the street to the left, this is where most car rentals are based
Practically you will stay on one street for about 12-14 km...

Anything you want to know, just ask

I did the opposite in 2008... picked up in central Athens and dropped a week later at the airport.

Clausar has given you good advice. I'll add a few things:

- Don't fall for the 'bring it back empty' option... you will lose unless you return the car running on fumes.

- Make sure you have an International Drivers License

- Greeks are enthusiastic drivers. Be prepared for fadt moving traffic on the highways. Doing 140 Kph on the way to Corinth the only things I passed were dilapitated old trucks.

- On 2 lane roads, if there is a paved shoulder you are expected to put 2 wheels on the shouldet to let a faster car by

- Drivers will pass on curves and on hills... keep right on curves and hill crests

Don't let this put you off driving... I love to drive in Greece. I rented through EconomyCarRentals.com and the car was supplied by Avis. Apparently good deals are also available through http://www.budget.gr

Have fun!

Sorry... that should have been an IDP... International Driving Permit... available at autoclubs like AAA, CAA etc

Great replies. The tentative dates are out of ATH May 21, 2013 and back to Athens, City Centre three days later.

I noticed that Economy Car Rentals was mentioned. Their website noted a "drop at hotel within city limits" option. Has anyone done this...how did that work?

They also mentioned the "All Inclusive Zero Excess" option, has anyone booked that? Is it a prudent deal? What beyond their "All Inclusive" rate did they hit you up for at the counter?

Much obliged...bdj