(although I am not sure how big the public that finds this useful actually is) I now present the contact details for the Turkmenistan and Uzbekistan consulates in Istanbul (current as at early May 2003):
Gazi Eurenos Jadesi Baharistan Sokak, 13
Ph: (90 212) 662-0221
Best way to get there from Sultanahmet:
Take a train to Eshilkoy station (25mins, 1m lira) and ask. 10 mins walk from there.
Senit Halil Ibrahim Caddesi, 23
Ph: (90 212) 323-2037
Best way to get there from Sultanahmet: Taxi (30 mins, 20m lira). There is also a boat and buses, but these are better to use to get home, because the consulate closes early in the day.
It takes less than an hour to get the visa at either place. Take in the application form, your invitation, and a photo, visit the nearby bank to pay the exorbitant fee, and then come back to get your passport.
Both consultates close and 12:30 and do not open again until later in the afternoon, and since they are at least an hour apart, even by taxi, you will struggle to get both visas in one day.