There are a lot of unique places in Psirri (which is just next to Monastiraki). I like the feel of the area, the streets and restaurants and the shopping is more eclectic and alternative.
A few examples:
Nancy's Sweet Home: The cakes here are to die for:
https://www.nancysweethome.gr/
H ΩΡΑΙΑ ΠΕΝΤΕΛΗ: I like this restaurant, it is right on the plateia and they usually have live Greek music while you eat.
El Habanero: If you like smoking the occasional Cuban cigar, this is the place to get all things smoking!
https://elhabanero.gr/
Little Kook: This isn't really my scene but a lot of people seem to like it. It is a fairytale themed cafe which changes its theme every so often. It's very kooky!
https://www.facebook.com/littlekookgr
But the best thing to do is walk around and check out the shops and restaurants (as always in Athens!) and you might find that you grow to like this area more than Monastiraki.