In my opinion there is not much great place to eat near Falirou 9, in Makrigianni.
There are even some of the worst tourist traps in the area, all lined up on the main pedestrian avenue, Makrigianni Street, in front of the Acropolis metro station.
Mani Mani is the headquarters for American tourists, I always take a look when I pass its small terrace. I read that Rick Steves himself admitted that he no longer sets foot there..."too touristy" he said... :))
If you have the strength to walk a little from your hotel (5 to 10 minutes), go further south in the Koukaki district where there is, for example, the "Seawolf" restaurant (lots of fish on the menu ) .
https://maps.app.goo.gl/zpBqHKLPkGx3EgQ87
Less expensive and nicer in my opinion in terms of atmosphere, decor, the restaurant "Sfika" (the bee) Quite a few good grills
https://maps.app.goo.gl/GQK1FiiKqhPv4stY9
For a lively and local atmosphere in the evening you must go a little further South into Koukaki via Veikou or Dimitrakopoulu street (which are parallel to Falirou) until Georgiou Olimpiou Street. You will find quite a few bars and restaurants and excellent street food places there. If you don't like it, I'll refund your meal costs !
Even while walking you will see some restaurants along the way.
https://maps.app.goo.gl/N12QEFZVvPSY2qmk9
But you can also go to the Psiri neighborhood, very lively, with a mix of tourists and Athenians, full of bars and restaurants. You need to cross Plaka district and go to the other side of Monastiraki Square.
https://maps.app.goo.gl/7SjUjRLhHrFegbHz9
When eating in Greek restaurants, order appetizer to share between everyone. tzaziki, taramasalata, greek salad, saganaki, melitzanosalata, fava... etc. and order main dishes according to your choice. The main dishes are brought even if you have not finished eating the appetizers.
Desserts are generally not on the menu (except in very touristy restaurants). At the end of your meal you will be brought something sweet, usually homemade. Or an alcohol (Tsipouro), or both! It's free .