Shang Tea is not a tea room. It is a fantastic tea shop with extremely high quality teas from China. Mostly white teas but some green and a couple of red (black). The staff are very knowledgeable, helpful and friendly. They will cup a tea for you to try and they will take the time to talk to you about it.
This is not really a tea room but more if a tea shop. The girls were nice & helpful. Their stock is stored in clear glass jars and doesn't seem to be very high quality. In addition, though nice, the girl assisting me had no idea where the black tea base in their flavored tea came from and looked at me blankly when I asked for details on the Darjeeling on offer. Prices were okay but the quality was lacking. As far as I can tell they didn't have food.
Tea Market is not a tea room, but rather a tea shop. They do not prepare tea here, nor do they serve food. Their selection of teas is more than appropriate and the quality of their offerings is excellent. They do have classes here from time to time where they serve food as well as tea and they have all been high quality and informative.
Teapot & Coffee House is a very nice place. They have 100 loose leaf teas available and very, very good scones. They offer other actual food, but I haven't tried it yet. I did try a spoonful of truffle ganache though and it was excellent. Super, super nice folks here. Their prices seem very comparable to other locations in Kansas City. They do seem to be lacking a bit in ambiance. The downstairs decor is very sparse. They may be going for monkish, but it doesn't come across well if that is the case. But as a place to get a cuppa and a scone, it is very good.