Emirgan Park
Situated on the gentle hill overlooking the neighbourhood of Emirgan and the Bosphorus, Emirgan Park was for long the only place in the city where Istanbulites can admire the beauty of tulips. Having lost that distinction in the last decade as tulips are now everywhere, this is still a beautiful park with artificial ponds, small waterfalls, and impressive views of Bosphorus. There are also cafes with open-air sections housed in pleasant former imperial hunting manors. Squirrels are there, too, in the middle of this metropolis of 15+ million people, though you may have to look a bit deeper or a bit upper on the branches! to spot them.
Maçka Park
This is a park occupying two sides of a valley of this hilly city, with an avenue inbetween. Sides of the valley are connected to each other by a 4-person gondola lift line offering a shortcut when walking to Taksim Square as well as nice views of Bosphorus access to northern station from Maçka Caddesi/Eytam Caddesi, every 5 minutes 8AM-8PM, 1.50 TL pp one-way, and by a wooden bridge over the bisecting avenue if you prefer to take a stroll along nice footpaths of the park.
Ortaköy
A neighbourhood on the bank of Bosphorus with the Ortaköy Mosque—the baroque mosque under the Bosphorus Bridge, combination of which are one of the most iconic images of Istanbul. This artsy neighbourhood is filled with nice cafes, some of which offer kumpir—a baked potato with various fillings such as mayonnaise, ketchup, pickles, sweetcorn, sausage slices, carrots, mushrooms, Russian salad among others—which the neighbourhood is well-known for, and a perfect view crowded and fun. The way from BeÅiktaÅ takes around 25 minutes on foot and is along an avenue shaded by huge plane trees, though the usually-heavy traffic may take some of its peacefulness away.
Rumeli Citadel
Built in first half of 1400s, this is the large medieval castle under the Second Bosphorus Bridge. Its former name BoÄazkesen Turkish/Laimokopia Greek means both "strait-blocker" and "throat-cutter" in both languages and denotes the reason of its building—to shut the supply routes from the Black Sea in the north into the slowly falling apart Byzantine Empire through the Bosphorus. Rumeli, literally "Roman land", was the name of the European half of Ottoman Empire, and as is usual with some other structures and villages along the Bosphorus, used as a prefix to differentiate Rumeli Hisarı from its counterpart in Asian Side, the much smaller Anadolu Hisarı, located just across the Bosphorus.
Sadberk Hanım Museum
A private museum housed in a yalı, traditional wooden waterfront mansions that lie along the banks of Bosphorus. Exhibition includes a number of archaeological and ethnographical artifacts from the collection of Koç Family, though just seeing the interior of a yalı is worth entering.
Sakip Sabanci Museum
Museum with a rich collection of calligraphy and paintings. It also hosts temporary exhibitions of works by some world-class artists such as Pablo Picasso from time to time.
Akaretler Street
Akaretler Caddesi, or officially Süleyman Seba Caddesi features upscale garment boutiques, restaurants, and sidewalk cafés housed in recently renovated late Ottoman era rowhouses initially built for the state elite, given their proximity to Dolmabahçe Palace, imperial headquarters then.
Dolmabahce Palace
It's the Ottoman Palace centered close to Taksim at the Dolmabahçe shore. Build on 110,000 meter square ground with 285 rooms and 43 halls where the Ottoman empire was administered in the last 150 years. Visits only in guided tours 45 min in major spoken languages. Extra fee for Harem, the part of the palace the residents lived, expect waiting some time for another guided tour there. The Dolmabahce Palace is definitely not as nice as one would expect for the hefty cost of 40TL per person as of Dec 2011 20 TL until recently. No photography is allowed inside the palace. Also important note, especially for photographers with large bags/backpacks: you may be asked to leave your backpack in the cloakroom, even though you're not supposed to know it before you stand in a 40 minute line to the ticket office.