Khiva has generally escaped the worst of Soviet architecture although the post office is an obvious exception. A large clock tower permanently stuck at the time five minutes past twelve serves as a useful, if ugly, landmark and a nesting site for hundreds of birds. The building's one redeeming feature is the wooden doors originally carved by the Mennonite Germans who lived in the nearby village of Okh Majit up until the 1920's.
The post office is the place to come for making phone calls and sending letters and telegrams but be warned - it continues to be a flourishing enclave of 'Sovietdom' with all the bureaucracy this entails. In theory it's possible to place a telephone call at any time of the day or night and this includes international as well as local calls. The receptionist, behind bars, takes your number and makes the call. You must then listen for her to yell your city or country along with a corresponding booth number where you dash to receive your call.
Usually there's no problem posting letters although postcards sometimes need to be sealed in envelopes. Every so often the attendants have pretty collector's stamp sets and it's worth asking. As for plans to send a parcel - don't do it. Whatever you wish to send, take with you and pay for overweight luggage on the plane if need be. Otherwise allow at least fourteen days just to obtain the neccesary stamps, documents and warranty to send the package in the first place.