All three places are quite touristic, so "authentic local culture" may be difficult to come by. Samarkand is a much larger, more modern, and prosperous feeling city, so there is probably less traditional atmosphere, but in many ways it might actually be more authentic in terms of reflecting how people live outside the tourist industry. The historical buildings in Samarkand are very nice, but highly reconstructed and bear little resemblance to how they looked even 50 years ago. I put some visual comparisons up when I wrote about Samarkand:
http://silkroadwanderings.blogspot.ca/2 ... rkand.html
Khiva's walled city may look the most traditional, but it's also probably the most intense concentration of tourism. So things might look traditional or "authentic," but you don't really feel from walking around that you are seeing normal locals living normal lifestyles. Much of the architecture and minarets in Khiva are much newer than in Samarkand, and as such are less restored and more "authentic," but for the most part are still less impressive.
Bukhara is also very touristed, but for me it is the best of the three. I think the largely monochrome brickwork makes the architecture feel less restored and Disney-esque, and the city is large enough (and the sites spread out enough) that it feels like you can breathe and maybe get a sense of more normal life as you walk to sites on the periphery of the city. I still don't think you're getting a really authentic picture of Uzbek life—especially in the most visited areas—but it definitely has the best atmosphere for me.
In my opinion the best way to get an authentic slice of life would be to visit somewhere where there are few or no tourists. Local markets are a decent choice in many places, especially if you go to a smaller one that tourists don't visit that often.
