If you're looking for high end Greek, check out Estiatorio Milos or Fig & Olive Restaurant

Middle ground: ilili or Pylos

For a more casual bite, you've got to go to Uncle Nick's Greek Cuisine. Or the ultra casual falafel spot Mamoun's

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For Greek food you should really venture to Astoria, preferably Taverna Kyclades BUT if you must stay in the city, I've heard wonderful things about Pylos

Molyvos is also quite good. It's more upscale and better if you're doing a business lunch.

Periyali and ilili are delicious Greek/Mediterranean options in Flat Iron. The grilled octopus at Periyali is perfection! I like Molyvos as well, but they are in Midtown and do not serve lemon potatoes during lunch, which is a deal breaker for me. Enjoy!

Astoria, Queens is where to find it. Aliada is what I recommend.

Go to Ethos on 33rd and 3rd.  Very authentic and good.

Milos Cafe is by far the best Greek in Manhattan. The pre-fixe lunch menu is a steal-http://milos.ca/restaurants/new-york/menus/lunch--2  One of the options comes with a little spinach pie but for $27.50 per person for the whole lunch, you can afford to get an extra one of whatever you want more of on the side.  It's up a little higher than you requested on 55th between 6th and 7th but it is worth it.  Very airy and pretty decor...white umbrellas like Mykonos, and lots of the staff is actually Greek.   

Kefi Restaurant is a great Greek restaurant in the Upper West Side. Kind of place where every dish is delicious and the value is even better. Worth a look.

HI Courtney I don't know anything about Lunch BUT.........

But there is an amazing and authentic Greek Pastry shop in Hell's Kitchen on 9th avenue in Manhattan. It's called Poseidon Greek Bakery

 It's got a lot of history and the best damn Baklava. The lady has owned it for years and her parents owned it before that.  She runs the bakery with her sons now.  Stop in for some pastry and a chat and then head over to one of the many bars on the strip for a cocktail.

Enjoy!

Tessa