Salonika's is good in a pinch. I always find myself here when I have tickets to an 8pm show at the theater and I'm just rolling into the 6th Ave parking garage at 7:20, hungry, and without a reservation to any of the more popular downtown dinner spots (Sometimes I'm bad at planning).
It goes a little something like this: Order at the register, pay at the register, take a seat, wait 5 minutes for food to be delivered, inhale gyro and BAM! I can make it to the theater with enough time to find my seat and browse the playbill. The gyros are pretty good. I prefer mine with about half the provided onions and with the gyro sauce on the side so I can really slather it on. The staff here is always friendly and the prices are reasonable. This is an A-OK place all around.
Bonus: they are open fairly late. So if you haven't left yourself any time to eat before a show in the cultural district, you can stop in after the show is over (Yup, I've done this too when I'm EXTRA terrible at planning).