If you are uncertain whether Szechenyi Spa Baths is women only or men only, or which days you can visit the famous thermal spa baths and pools, the answer is very simple: Szechenyi Baths is mixed, all day, every day. Hence you will be kindly asked to wear swim suits. It is prohibited to use the baths, pools, saunas, and other facilities without a proper swim suit (e.g. trunks for gents, swimming suits or bikini for ladies).
You can sunbathe in the outdoor gardens and by the pools (you can even rent sunbeds for sunbathing) but even if you are only sunbathing in the courts, please keep your swim wear on.