1. Get an Istanbul Kart. This card unlocks public transportation from metro to buses to ferries (by the way, check out how transportation works here). Not only will you avoid the appropriately infamous traffic, Istanbul's ferries are an experience of their own. Cruise the Bosphorus while sipping a Turkish tea. Pick up the famous yogurt with powdered sugar in Kanlica. Wish you went to work this way every day.
2. Lahmacun, kofte, kebap. Turkey's meaty favorites are delicious, inexpensive and ubiquitous. Each of these is described in more detail here, along with a few other cheap stomach-fillers.
3. Mosque-hopping. Many of Istanbul's most beautiful sights are free. Make it your mission to decide which of Sinan the Great's impressive structures is your favorite. (Who's he? Learn.)
4. Istiklal. This walking street through the heart of Beyoglu pulses day and night. Have a wander, watch some street performers, and climb to a second-floor cafe for a tea-and-sweets break when you're overwhelmed by the crowds. More on Istiklal here.
5. Find free art. Istanbul's burgeoning gallery scene gives you access to ogle art for free. And, you will get a glimpse of the city's contemporary side. Visit my favorites.
For more detail, check out the Frugal Traveler's take from the NY Times Travel Section.