I need a travel agent who:

Can deal with complicated itineraries to crappy places on crappy airlines (can get tickets on Ariana, for example);
Speaks English
Accepts modern forms of payment (ie foreign credit cards)
Is reliable.

Any suggestions? Moon?

I don't think you can tickets to the moon here but a lot of the agencies near the tramway at sultanahmet are good. i.e Marco Polo travel, I've used credit cards with them in the past, most of the offices along there have excellent English speakers as foreigners are their core business.