There's a new place for coffee and tea in the centre of Budapest at Nádor utca. The place is called Kávétársaság (something like 'coffee society' in English). It doesn't only serve tea & coffee but also sells them as well as high-quality coffee machines. The shop for the machines is downstairs. You can find tea, coffee and other items related to them in the middle of the shop.
Tried there White Pai Mutan tea by Swedish Johan & Nyström - also available in the shop! - and Northern Berries by the same company. Both excellent! And the gluten free chocolate cake was heavenly!
The interior of Kávétársaság is really beautiful and well-made. Lots of black and white - my favourite combo - and a hint of colour in the floor tiles. Gorgeous custom-made mirrors and nice pendant lamps hanging from the high ceiling.
Pop in when you're in the neighbourhood!
Nádor utca 14, V Budapest