Tuzla Garden Hotel & SPA
If you are staying in Sultanahmet, this one is a separate outing rather than a stop between mosques. Tuzla Garden Hotel & SPA is a hotel whose spa sits inside the building, at Galip Ağa Sokak 22 in Tuzla, around the Postane area. Google shows 4.7 from 362 reviews. The listing says open 24 hours every day, but it is not clear whether that applies to the hotel or the spa. I could not read the hotel's website, so treatments, hamam, pool, sauna, prices and whether non-guests are admitted are all unconfirmed.