I loved my visit to the Szechenyi baths. It is definitely a must do when in Budapest if only for the experience of the grand old building! Visiting during the colder months seemed a good choice as the place wasn't too crowded and being able to warm up in the outdoor pools was lovely.
At first we thought the entrance fee quite expensive - especially compared to the cost of other things in the city, but then once inside it is a large complex and you could easily spend the much of day there. Additional spa treatments looked quite pricey as well so I think it is very much the 'tourists' baths and priced as such. I would advise saving money by taking your own flip flops, towel and swimming cap (for large outdoor swimming pool). Even on the cold day we visited I am not sure hiring a robe is needed unless you really feel cold.
The place is a bit 'tired' and could probably do with a bit of a deep clean and spruce up. Some of the pools seemed not as clean as they might be with bits floating in them, perhaps more regular cleaning is required given how many people use the baths each day. (Having said this I am an anxious cleanliness obsessive and it wasn't enough to put me off so really not too bad!).
Overall, I loved my relaxing morning and can't wait to return at some point.
Tip - make sure you try out a couple of the saunas.
Also, don't let any of the reviews on the internet that mention finding your way around confusing or staff being rude. Staff were friendly and helpful and it's easy to find your way around and to work out lockers/ cabins etc.