Istanbul Shore Excursions are the best ways to explore this city. If you are in a real hurry or keeping your budget tight, here is the best option for you..
If you want to go the ultra budget route or if you are really in a hurry, get on one of the motorboats from Besiktas to Uskudar.
Walk around in Uskudar, see the wonderful mosque right next to the port, then get back to Besiktas.
This short cruise will cost you only a few TLs. It is short and not very comfortable but it is cheap, and you get great views of Istanbul.
One major tip: Sit at the back of the upper deck. This way you'll get great vistas on both sides.