Although the Hungarian cusine is not particularly renown for vegan dishes (Szálámi, Gulyás, etc...) the capital Budapest offers quite some opportunities for vegans. (Some are however a bit pricey, at least for Hungarian standards)
Near Batthyány tér (Metro 2 stop) you can find the restaurant. They are exclusively vegan and speak fluently English. http://www.edenivegan.hu/elerhetosegeink/ Address: Iskola u. 31. Opening Hours:
- M-F 8-20h
- Sa closed
- Su 11:00-19:00
It's close to Vörösmarty utca or Kodály körönd, and not that far from Keleti p.u. http://www.napfenyesetterem.hu/english Address: Rózsa utca 39 Opening Hours: M-Su 12:00-22:30
On the backside of the Kossuth Lájos Station. This place has amazing raw/vegan cakes. http://www.mannatural.hu/miert/ Address: Garibaldi utca 5 (down the stairs) Opening Hours: M-Su 11:00-21:00
There are multiple Hummus Bars in Budapest, where you can buy vegan falaffel (with student discount).
It is quite common in Budapest to buy food at a market (at a "piac"). There are quite some markets and usually it is cheaper than buying at a supermarket (esp Spar...).
Actually it is closer to Fővám tér, but sort of inbetween both, and the connection to Kálvin is just way better. This is the so called big market hall, and whereas upstairs you can find (sort of expensive) souveniers, downstairs you will find the food. There are multipe lines, one is more expensive, the other sort of cheaper. Usually the offers at the other places are cheaper :)
The 2nd big market building, actually in the shape of a boat. You can find pretty reasonable offers here, but usually at the side of the building not in the main rows.
At Rákoczi square you find another elder market building, inside it's again the same old game: The central booths are more expensive, sell somewhat higher quality, the others are cheaper. (Check: 1kg Tomatos/Paradicsom should never be more than 200HUF)
There are other smaller markets, e.g. at Teleki tér (quite cheap, lower quality) and sometimes near Keleti p.u. people try to sell vegetables w/o having a license (very cheap, but you know why ;))
If you go shopping somewhere, important things to look for are "tojás nélkül" (without eggs) e.g. pasta "tej nélkül" (without milk) Other important words are méz (honey), hús (meat), tej (milk, not to confuse with "teljes" as whole in whole grain), tejszín (sour cream), túró (cottage cheese), vaj (butter).