Side note on Turkish pronunciation: ş is like sh, ç is like ch, and ğ is silent (lengthens the preceding vowel). And a c is like a j. More on pronunciation later.
Thus Chicago is spelled Şikago (as I saw it on the baggage carousel at the airport, when my luggage didn’t arrive at first).
After a late start, I took a tram across the Golden Horn (river) to Beyoğlu, where I met Ahmet, a friend of a friend of a friend, for coffee in the middle of Istiklal Caddesi (Ave), the heart of the modern city. Thank you for the pointers, insights and pronunciation tips! (e.g. the name of a good leather jacket shop in the bazaar, local blue fish is in season, and a multi-day muslim holiday starts on Sunday – oops).
Istiklal is a busy, quasi pedestrian-only cobblestone avenue with shops and restaurants, with an old tiny streetcar (reminiscent of a cable car in San Francisco) running down the middle of it, with no safety zone around it of course (that would be so North American!)
Otherwise spent the day walking and snacking 
Most common street sights I’ve noticed:
- Döner restaurants
- Sweets stores
- Fresh fruit juice, esp. oranges and pomegranates (they must be local and in season)
- Roasted chestnut carts
More details than you probably care about:
I walked up and down Istiklal, had a nice veggie lunch, was finally able to buy an electronic transit card, the Istanbulkart, from the booth at the top of the Tünel funicular (no sign indicated that was possible, and the token machines don’t sell them either, though you can add value to cards via machines; thanks again Ahmet), walked a bit along the water in Karaköy where I ate a tasty fresh grilled fish sandwich (TL5/$3) from a streetside bbq-cart vendor and had the best baklava ever at a nearby recommended sweets shop.
I then took the funicular back up to Istiklal and meandered it at night. Tried to stop for a beer but was told “couples only” or “family only” (no single men) at two bars one block, where there was some live music (one guy on a guitar and singing) in no less than 4 bars. Sigh.
After taking the tram back to my hostel’s neighbourhood, Sultanahmet, I checked out the details at a nearby famous hamam (Turkish bath) for future reference, and I meandered through some side streets.