Walking out of the Tashkent airport at 3 AM, I was MOBBED by every cab-driving shark in the country. Unfortunately I had taken forever to get my airport visa, so all the others from my flight were long gone...so there was just me and all these creeps calling me "dushka" (Russian equivalent of "hey, baby")
I hated them so much that I walked into Tashkent.
It's possible to do this, but probably not if you're carrying heavy stuff.
I got into the city itself, a couple of km, before I broke down and hailed a passing car. A ride anywhere within Tashkent should not cost you any more than $2-$3.
It's not hard to find your way into the city on foot, there's really only one road that leads to the big buildings, but even if you don't want to walk all the way (Tash is huge) you can walk far enough to get away from the sharks and find someone a little less dishonest.
Good luck.
You can withdraw cash with a Visa card in Tashkent, and I did it in Bukhara also. I paid a $3 commission to withdraw $100. Withdraw dollars no matter what they tell you, then exchange those dollars on the black market.
Current black market rate = 2200 sum / $1.
Official rate is something like 1580 sum / $1.
Don't ever change at the official rate!
Lots of people can change money at black market rate, if you're not near a bazaar, try a food shop or a jewelry store.