We have a group of 8 friends traveling to Budapest in early October and are interested in the baths. After looking at the website he best way to go about the baths is not clear. We are thinking we will go either on a Monday afternoon or Tuesday morning and spending a couple of hours there. My main goal is to enjoy the outside baths because the building is so cool. However, I would love any recommendations on best time of day, which ticket option we need, should we get a private changing room/locker or just change before we go, are there other cool baths to see, etc.? Our budget is flexible as well.
I would recommend that you go in the evening. That way you get to relax after visiting the city and tourist attractions during the day, and you can spend some time in the warm outdoors pools after sunset (it looks great with the steam rising from the water in the cold). Indoor pools close at 7 pm and outdoor at 10 pm. You could arrive around 5/6 pm, get to visit the indoor facilities and spend some time in the outdoor pools, both at night and day. Anyway, check the opening hours at reception in your hotel/hostel when you arrive, in case they are different in autumn.
Széchenyi Gyógyfürdő és Uszoda (Széchenyi Thermal Baths) are a great way to spend a few hours in Budapest. I would recommend showing up around 10 or 11 am. There isn't really a difference that I have noticed from one weekday to the next. The locker rooms are just like any public pools would be in the States. I would just get the standard ticket that includes the locker, no need for the private room. The lockers are simple gym style lockers for your footwear and clothes. There are several different pool options to explore inside and out, but I have had the most fun in the outdoors one.
Mentioned in this answer: