We always spend a couple of weeks in Greece in December, often in Athens, and often a week or ten days there in March as well. It’s a nice time of year to be in Greece - everywhere is quieter and it has a different feel - although the weather can be bad, especially in February.
Whether four weeks is too long in Athens is a matter of taste. We enjoy getting a nice apartment in an interesting neighbourhood, pottering about, going to local markets, getting to know local restaurants and bars, and generally not doing a lot. If that’s for you then four weeks is fine. If you want to be doing something different every day then it’s too long.
If you do opt to spend a longish time there you can easily spice it up with some day trips: Delphi is lovely and Aegina worth a visit.
I second the suggestion of Nafplio. A beautiful town and easy to reach on public transport. We’ve written on our blog in (perhaps boring!) detail about how to do this
http://www.greekramblings.org.uk/Nafplio_getting_there.html
There are lots of good Airbnb places in Athens and a handful in Nafplio.
Thessaloniki is interesting but is further north and will be cold and likely wet in February and March.
A lot of the islands are very quiet at that time of year but Crete is lively and you could easily spend a couple of weeks there.
Alan