Authentic Hungarian goulash

James E. will reply to your question with an authentic, reliable and accurate suggestion. Whatever he says....do it.
My humble recommendation is Hungarikum Bistro (Steindl Imre utca 13, district V M3). Near Parliament. Family owned, friendly and fabulous.
Make a reservation or you'll never get in. Seating capacity is about 25. I love this place.

If you already know this, ignore the following: "authentic Hungarian goulash" is a soup, not a stew. The stew has different names; one that comes close to what we in the US call "goulash" is pörkölt.

The soup is good; the stew is fabulous, everywhere I tried it. I was there 10 years ago, so I'll let James give you current recommendations. But do realize it's a common dish, available all over, and I'm not sure I'd make a special trip just for the "best" (sort of like those lists of "best hamburgers").

P.S. -- if you have cooking facilities, you can buy canned goulash soup at a local Sparmarkt. Not the "best", certainly, but a good cheap meal you can eat in your jammies.

Geeeeeeeeeee, how do i follow that?

It actually very good in most places. There are to variations, one with potato and one with spatzle (csipetke). I think the spatzle version is more historically accurate. I've had it at Hungarikum Bistro and it was very good. Also good at places as varied as Vakvarju (lower end of Ede Pauley utca) and Belvárosi Lugas Vendéglő (across the street from the back of the Basilica) all have good gulyás (sometimes on the menu as Gulyásleves which literally means goulash soup). Dont think i have ever had a bad bowl anywhere, just some better than others.

Since you are at it, you need to try Toltott Kaposzta (stuffed cabbage). A bit harder to find, you can get a pretty good taste at Belvárosi Lugas Vendéglő; and surprisingly the Panorama Teresz on the Danube Corso and Csarnok Vendeglo on Hold utca.

Oh, and dont forget the Palinka!!!

Ah, stuffed cabbage! Best meals I ever had on a RS tour were the stuffed cabbage in Hungary. Didn't think I would like it, but I loved it.

And its usually served with a big chunk of fried pig fat (skin on). Mmmmmmmmmmmm!!
Also keep in mind that Hungary has the highest per capita consumption of duck liver. Also very good with Tokaji Aszú 4 or 5 Puttonyos. Ahhhh, the noble rot is so sweet!

Thanks so much for the help. We are very excited to experience local dishes in all our stops on this trip.

Agree completely with Blue439. Hungarikum Bistro was our favorite in a week of wonderful food in Budapest. When we wondered whether we both wanted a bowl of soup and a large meal, the server said, “Well, if you like I can bring one order and will divide it among two bowls.” When did that ever happen to us? Everything was delicious, the prices were right for us, the staff were so friendly, the owner visited our table to chat and check, and the cimbalon played on. Added bonus: a cheerful handout shares their “Recipe of the Goulash Soup”. I have made it several times since and we enjoy it. Reservations were necessary, days in advance, as is the case it seemed just about everywhere. Our hotel handled the calling for us. We returned later in the week for another excellent evening.

When calling for reservations yourself, just say good afternoon in English and 9 out of 10 times they will switch to English for you.

Yep, most of the younger Hungarians speak good Emglish. We often saw them out nights conversing in English--practicing on each other.
Their goulash is nothing like my mother cooked--I promise. The paprika we get is just not the quality of the paprika in Hungary.

A lot of tourists buy paprika when in town. The tourist shops have paprika in real interesting packaging. But for actual use and not just as a souvenir, I think you might do better buying a fresh tin off the grocery store shelf.

In a grocery store in Budapest, when a customer saw us humming and hawing over a paprika purchase, she advised us to look at the “best before” date. It may not have been termed “best before” (can’t remember) but it was a date that indicated the paprika’s freshness.