Hello Chani, you know what I am going to say: "I will see if I can plan my trip for the same days"
Sorry, I am not well enough traveled to say which markets are the best in Europe; that would require I go to a lot more markets, but I can tell you my impression and the few details I know about the Budapest market.
First there are two major markets, one at Vorosmarty ter and the second at Szent István tér; and you know where both of those are (a 5 to 7 minute walk between the two).
There may be a few booths set up elsewhere like Nagymező u in front of the Operett Theater and I think maybe on Frans Liszt ter; but if they exist they are really secondary; and there is a fairly large one in the square in Obuda which is more "local" in flavor and less touristy..... (M2 across the river then the H5 to Obuda)
Next, everything at Vorsomarty ter and Szent Istvan ter will have been reviewed by a committee to ensure they are all local products, arts and crafts. No imports allowed.
Food Stalls generally close on Christmas eve, but the vendors stay until New Year's Eve (and they were open last year so I have no doubt they will be open this year starting the weekend of the 18th of November I suspect).
https://www.youtube.com/watch?v=BvylwDspV9o
https://www.youtube.com/watch?v=f_L0Xp6b2R4
https://www.youtube.com/watch?v=lLy0mHxrXkA
And the one in Obuda: https://www.youtube.com/watch?v=oUTpQhHMqk0