Pagabi1300, am hoping that -- because u want info about less-known sights -- this does not mean you want to skip the Arch. Museum. Some people are put off by the idea of a huge store-house you may get lost in... and just like the NYC Met, or other European Museums, one can be overwhelmed. But I'd hate for you to miss out for this reason -- because you're in luck! This very website can give you a step-by-step DIY Audio tour of the "top 10 don't-miss" treasures of the Nat. Arch Museum. Rick Steves has an "Explore Athens" page where you can download this tour FREE -- https://www.ricksteves.com/europe/greece/athens Please note also his FREE audio tours of the Acropolis AND the Ancient Agora... PLUS a DIY walk around Athens. I've told many people about these treats, with great feedback. Besides helping you get the most from each of these sites, it enables you to do it at the time YOU choose, rather than a group tour schedule.
As for other Museums, if you are not going to be in Cycladic Isles like Naxos or Paros, you can view very ancient finds & learn island history at the Cycladic Museum, just off the far side of the National Gardens... it has fascinating marble figurines whose use & meaning is still a mystery. Its top floor also has a short & well-done video about how families observed customs & traditions during the "golden Age" of Greece and Athens. And of course, don't miss the Acropolis Museum itself ... again, your experience can be enhanced by starting at the TOP floor, which has an excellent video of the Acropolis/Parthenon story, with animation AND reinactment, plus rebuilding/repair footage. If you haven't done advance prep, this helps u get so much more from the exhibits.