Car Rental Athens

I am doing the exact same thing- Renting a car in Athens for four days in October to visit Meteora after our Rick Steves tour.
I am picking up my car on Syngrou Avenue, since it's walking distance from our hotel, and then returning the car at Athens airport. I booked thru Costco Travel - who booked me through Sixt.
No deposit paid, but I guess they have my credit card.
In direct answer to your question, I have not heard about Swift, so no experience.
I have booked rental cars for Europe and the US through Costco Travel and have always gotten a good price. I've never paid a deposit.
Good luck.

I rented last summer through an American travel company called Gemut (gemut.com).
They deal through a broker : Auto Europe

Gemut gave me by far the best price for my Greek car rental (better than the quote I got from Costco). They have an American service desk you contact if you run into any issues including language barrier (l found little of that in Athens) or if there's something not quite right at the rental counter.

You do pay in full at time of booking, but that has been refundable in the past almost (or even maybe all the way) to pickup date/time.

I've never had any problem with them.
Worth at least getting a quote and comparing

I WOuld advise checking reviews on Swift, maybe thru Trip Advisor, also other sources. There have been reports of older vehicles, malfunctions, etc. THis may be something in the past, but it's best to investigate. In past forums, I see that Economy Car Rentals is recommended -- while Economy Car Hire was warned against. Since I've always used ACR, I cannot comment. FOrum vets from UK have often Mentioned Auto Europe, also.

See the details of bad experience with Swift in the Thread title "Is a Car Necessary for Nafplio?" Also that thread gives a very positive review for Gemut, thru Auto Europe.

Just returned from Athens after having rented from these guys. Terrible experience and I would just avoid it. Paid for a bigger car and ended up with a tiny Nissan micra with 70K kilometers. When I constant swift, the guy out rightly refused that my booking was for a bigger car. Car reeked of smoking and felt like transmission would just not last full two days. Cant trust these guys and I wish I would have paid an extra 20-30 euros to just rent from reputed companies that do business worldwide. You can’t return car early because they have a schedule for pickup and return. Absolutely horrible experience and If this post can help someone avoid these guys, it will be best.

Swift Avanti was really good for us. They picked us up at our hotel, drove us to their office on Syngrou to do the paperwork, and pointed us the way to get out of town on the highway. We dropped the car at the airport, and they had someone meet us there to do the return paperwork.

We too got the suggestion from Matt Barrett's guide. My experience is that everything Matt says is more reliable than anything you'll hear here or anywhere else.