The Uzbek consulate in Tokyo unfortunately does not have a usable website (in Japanese, let alone English). You have to fill out your information at the website below, print it out, and give it to the consulate. Make sure that you mark Tokyo as the place of visa issuance. Under Occupation ‘Representatives of business groups and persons, engaging in individual enterprise’ is what most folks put (I’m an engineer damn it!)
Cost for Americans: ¥16000 JPY for a 30 day tourist visa (maximum) is super pricey, so make every day count. You can ask for as many entries as you wish without a LOI (but be specific (i.e. 2, 4, 7, etc); putting ‘multiple’ will mean a LOI will be required). Note that this is paid in cash at the time of visa pickup!
Website: Ministry of Foreign Affairs
Hours: 10:30-13:00 for drop off, 16:00-17:30 for pickup.
Contact number: +81 3-3760-5625
Map: The Uzbek Consulate is located a few blocks from Fudomae station (past Meguro on the Namboku line).