Beyoğlu's art spaces are all within walking distance of each other and most cost nothing. You can see three of them comfortably in an afternoon.
Pera Museum. In Tepebaşı, one street west of İstiklal. The permanent collection holds Osman Hamdi Bey's *The Tortoise Trainer* — the best-known painting in Turkey and genuinely worth the trip. The collections of Anatolian weights and measures and Kütahya tiles are there too. Two floors are given to temporary shows. An hour is enough, two if it grips you. Closed Monday, open late on Friday evenings.
Salt Galata. The old Ottoman Bank building, on the slope down to Karaköy. Exhibition floors, a research library, and an enormous reading room you can walk into and sit down in. Free. The basement, where the bank vaults are, is an exhibit in itself. Closed Monday.
Salt Beyoğlu. The same institution's second building, on İstiklal. Smaller, more contemporary, usually built around a single show. Free, and half an hour does it — go in if you are passing.
Akbank Sanat. On İstiklal, quietly good. Exhibitions, concerts and film screenings. Free.
Arter. In Dolapdere, slightly outside Beyoğlu but ten minutes from Taksim. A new building, a serious contemporary collection and five floors of exhibitions. Ticketed, but free on Wednesdays. Closed Monday.
Suggested route. Salt Galata at the bottom of the hill → up to Salt Beyoğlu → Pera Museum. All three are walkable and this order makes you climb the hill once rather than twice.