I have 3 full days in Budapest to dedicate to seeing how non-tourists live. My ideas so far are seeing some of the other market halls other than the Great Market Hall, and maybe some baths other than Szechenyi. Thoughts? Thank you!
Head to the Buda hills for a walk and great views via the Zugliget chairlift and the funicular railway.
There are plenty markets and flea markets particularly at the weekend.
Those are two good ideas, the markets especially on Saturday.
Find a walking tour published online for Jewish Budapest as a lot of that is off the beaten path.
I enjoy cemeteries too and Budapest has two excellent ones that are in "interesting" parts of town: https://zsidotemeto.nori.gov.hu/ and https://fiumeiutisirkert.nori.gov.hu/.
Or just walk up Andrassy ut past the Octagon and turn right or left at any point and you will end up some place interesting.
Or get on a tram or metro and stay on till you are beyond the typical tourist spots. Try District XII.
But do be aware that, outside District V, the "tourist" areas are truly living and functioning neighborhoods, not Disneyland like Prague Old Town (for instance).