Only the rest of the day left and baths are a priority with no preference which. Also would like to experience great Hungarian wine.
We had an thoroughly enjoyable wine tasting experience at Taste Hungary. I reserved it several weeks ahead of our visit. https://tastehungary.com/tour/wine-cheese-charcuterie-tasting/
Okay, so 11/30 is a Monday. Thats good as Szechenyi Baths might not be too crowded. Szechenyi Baths is sort of the gold standard for the cultural event.
Two other choices that I can think of are Lukacs Baths https://www.lukacsfurdo.hu/en This one is where more of the older locals go. Few tourists but a fair number of expats. Less expensive and usually less crowded, but this is where you go for a totally different and less glamerous (but incrediably eyeopening) experience. Most of it dates to the 1880's. My favorite when I ache.
The other that comes to mind is near Lukcas and its called Irgalmasok Veli Bej Bath and it is one of the ancient 500+ year old Ottoman baths. I will be honest, I havent been but I will befor this year is out. Recently renovated and looks beautiful. Smaller so I dont know about the access: http://www.irgalmasrend.hu/site/velibej/home run by a catholic religious order. Terrible website. So this is what it looks like https://bathsbudapest.com/veli-bej-bath/veli-bej-interior-bath-budapest and https://contentf5.dailynewshungary.com/wp-content/uploads/2018/01/termalfurdo_veli_bej_irgalmasok_6.jpg
For the wine, a wine tour is great. I also know a private wine guide that I really enjoy. She would take you to a wine bar and walk your through the wines for as long as you like. The advantage is that she can get you away for the thick of the tourist wine bars. Budapest by the way is stock full of wine bars and wine events. Its in the blood here. Unless you wanted to visit an winery. There are some within an hour of the city and she has contacts for setting up tastings.