I don't have anything specific. I lived there for five years, and only learned basic-to-midlevel conversational Hungarian (although my food, especially ingredient, vocabulary got quite good: better than my co-mother tongue Polish.) It's a pain-in-the-ass language, and supposedly the most difficult Roman alphabet language to learn for an English speaker. (I would guess Finnish is probably right up there.) Then again, like all languages, it's something you can learn through intense immersion. I have a friend who was monolingual before he came to Hungary when he was in his early 20s, ended up living somewhere way out east where there were no English speakers around, and managed to learn the language by going to the bars for a couple of years. From what natives tell me, he has absolutely no trace of foreign accent when he speaks--just Eastern Hungarian. So it's doable.
But I really don't know what resource would be best. You can probably start out with some tapes or something, but you really need to interact and talk with people to really get it down. I believe there are online video chat resources that deal with language learning, where you exchange your English skills for somebody else with their language skills. I would think that would be quite helpful. Or I wouldn't be surprised if you can find someone from the Hungarian community here who offers those types of services. There is also a
meetup group, so it might be worth checking that out, too. I'd also consider calling either St. Stephens of Hungary Church here in Chicago or the Norridge United Church of Christ and see if they have any leads.
Regardless, you can get a taste of it by starting out with
something like this, and then I strongly, strongly, strongly recommend finding ways to actually use Hungarian with other people as soon as you can.