THE place for puerh in Budapest. (Maybe in all of Hungary!) Levél has a huge collection of puerh teas and a huge sortiment of teawares too. Wonderful cakes to try, buy, or drink on the spot. They have a little room for drinking tea, the whole place is quite quiet, so it would be ideal for dates or small meetings.
If you are looking to buy tea, be prepared with your specific preferences as the owner, Liu, does not speak English or Hungarian, so you won’t be able to have elaborate conversations about your preferred tasting notes. :)