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
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.