Hungary has come a long way with excepting people who live an alternative lifestyle.
We personally know several "gay" men who are Hungarian that left HU in the early 1970's and came to the US.
My husband is straight but he knew these guys from the refugee camp they all lived in and we used to run into them at parties etc. in Cal.
I also was a teen runaway in the early 1970's and my male gay friend gave me shelter and was my big bro looking out for me. I am straight but found a home and a huge welcome in the gay community as a run away.
Hard to explain why and how many gay men acted like my older brothers looking out for me, feeding me and making sure I went to school taking me clothing shopping and just being there for me.
I suppose I was a pet project.
My older sister introduced me to her gay friends, female and male, she was bi-sexual. I was taken in as a kid ,they all guided me until I moved on with my own life as a young adult.
For a full year of my life all I knew were gay men.( 1972-73)
As senior aged straight long time married people we don't actually know what is going on in Hungary these days with gay society.
I would suspect one way would be to go clubbing and check out clubs on your own, I do believe some spas have men only days.
3 years back we went to SE Poland so I could meet my father's side of the family that still lived in Poland.
I was rather surprised to find out my 2nd cousin who owned the B&B we stayed at was gay and he and his partner owned and ran the B&B.
Met another couple from the UK at our family reunion who were gay men, one was also a Rusin from that area of Poland and his partner was British.
I was surprised because I also thought Poland was very hard on gay people, with my cuz living in such a small community and being excepted and having a thriving business was very interesting.
Times have changed. No one in our large group of 16 people said a word in the negative about their set up, either times have changed or I come from a very open minded family of people.
Really I would just suggest living your life, going to places you enjoy and if you meet like minded people while doing activities you enjoy then that would be great.
Join the book clubs you want to, gyms, play sports and if you happen to meet new friends then so be it. I have meet many gay people just doing things I like doing and I am not even looking to meet them. You and your partner should just move to HU if you want to and be ready for anything. There used to be a so called,"Love Parade" every Aug. in Budapest, we used to just bring a chair and sit on the sidewalk with a cold beer and watch the floats pass by, later people started calling it the ,"Gay Parade" and many idiots threw rocks and bricks at the floats, the police had to put up wire fences etc. These days the parade is no more, really sad because all sorts of people used to come out, dance in the streets and listen to the music.
Not sure why HU was so open at first then got all red neck and conservative.