Travelling between Tashkent, Samarkand, and Bukhara will be easy enough by train. Khiva, like mentioned, is a bit more difficult because you would usually transit via Urgench. Personally I've found shared taxis pretty safe - just try to find out what the price should be before you get in, and preferably from a local who's not the driver. Khiva, Bukhara, and Samarkand are all walkable, so getting around the sites should be pretty easy, though Samarkand is much more spread out. Tashkent has an excellent metro system. Since you don't have a lot of time, you might want to consider either not going to Khiva, or getting an idea of where to spend more of your time. In a crunch, Khiva and Bukhara can each be experienced pretty well in one full day (e.g. 2 nights) since their sites are within old city walls. Bukhara is slightly more spread out. Samarkand should get at least 2 days / 3 nights, Tashkent 1, maybe 2 if you like cities a lot. My favourites were Khiva for the sites, and Samarkand for the sites (Registan, Shah i Zinda, Ulug Bek observatory & museum) and general vibe.