Dredging up this year-old post b/c we just got takeout from the Great Neck loc. I highly recommend it (at least for takeout!). Ordered chicken kebob plate, spanikopita, greek sausage app., and giant lima beans (and they threw in some of that custard-phyllo dessert). This was seriously good food. Chicken served w/ lemony rice and very freshly steamed veggies. Limas were in a light tomato sauce, and everything was just quality and fresh. The sausage is (apparently) house-made, and it's pretty coarse, heavily spiced (incl. orange peel). I think I'm addicted.
Which Mykonos are you asking about? The one in Great Neck is OK.
Unless you want to go way upscale, at Limani or Trata (both in Roslyn), it's as good as any others in the neighborhood.
The Turkish Kebab place on Northern in Little Neck is very good, btw.
1043 Northern Boulevard, Roslyn, NY 11576
37 Great Neck Rd, Great Neck, NY 11021