I have a chance to stay in Athens in an apt. in the area described bellow.
I don't have the exact address, I realize the place is ib one of the suburbs.

"It is situated in a quiet, safe residential neighborhood close to the new Olympic Stadium of Athens A few restaurants and cafés are within 2-10 minutes on foot from the apartment but you'll find countless more choices for wining and dining within a short 10 minute ride. The newly developed area around the Olympic Stadium (Maroussi), along with neighboring Halandri and Kifissia are also a shopper's paradise;
The neighborhood is also served by a free local bus that goes to the major traffic artery of Kifissias Avenue (less than 1 km/half a mile away) and the metro/suburban railway station "Neratziotissa".

Would it be difficult to get to the center by public transit?

According to the description, it should be located in the northern suburbs of Athens.
There is a green line station nearby ( Nerantziotisa), which is excellent. It takes 25 min to go to the center ( Omonoia square, or Monastiraki) and 5-10 min to go to Marousi or Kifisia , the posh suburbs of Athens full of restaurants shops and cafes.
If you could give us the name of the street, i could give you precise info about the location.

Thanks. I'll try to get the name.

I have never been to Greece.
We like museums and art, not interested in beaches
Would late April be a good time to go?
If we stay in Athens for several days (4?), should we then visit some of the islands
or stick to the north?
We don't wish to drive or move too much. 12 or so days on the ground.

Late April is a good time to visit Greece, especially the southern part.
The weather can be still a bit rainy, and it's getting colder the more up to the north you go.
4 days in Athens are more than enough, you should decide what you would like to do during the remaining 8 days.
You could either rent a car and make a Peloponnese tour, you would have enough time to see all the highlights such as Olympia, drive down to Pylos, then to Kalamata and through the messinian and laconian Mani to the beautiful medieval town of Monemvasia, heading towards north to Mystras and then Nafplio.
If you don't wish to drive you could visit some of the islands, the possibilities are endless.. there are the highly praised in this forum Santorini, Naxos and Mykonos followed by many other islands.
Just keep in mind that the weather will still be not warm enough for swimming, in general warmer islands are in the south such as Santorini or Crete or Rhodes.
Once you decide how you would like to spend these remaining days, we will be able to make more concrete proposals.

Thank you very much.
I will do some research , We are not interested in being on a beach or hot weather.although the island s look stunning.
I guess, without driving it would be hard to see some of the north?

do you mean North of Athens, or Northern Greece?
If you are not interested in beaches a Peloponnese tour would be ideal, as already mentioned there's a lot to see there, and weather won't be hot during the end of April, on the contrary it will be springtime and there will be flowers everywhere.....
You could also move from one city to the other by using public busses, the connections are excellent, but having your own rental car is much more comfortable, as you can stop where you like.

Thanks
I better do some reading to have more relevant
questions
Thanks again. I'll be back!