Take a cab for 20 min to Bostanci Ferry Station and ferry to Yenikapi. From there take another cab for 15 minutes.
Usually I don't recommend cabs due to traffic but you'll be commuting in lesser dense areas non-rush hour.
Exit airport terminal into a cab say Bostanci Iskelesi "Bost-ahn-jeh Isk-ehl-ehs-eh." You can copy this page and highlight the station names to show to cab driver. You arrive at 1:30 and by the time you clear customs, etc it s/b about 45 min. The ferry from Bostanci departs at 4:30 and makes one stop at Kadikoy before you exit at Yenikapi. Ferry trip time s/b about 30-40 minutes. You s/b at Yenikapi station around 5:15.
From there get in a cab and say "Buyuk Otogar" "Boo-yook Oh-toh-gahr".
Another choice would be to take Havas Bus (in front of airport terminal) to Taksim. and from there take a 15 min. cab to Bus Garage.
Bus ride takes about 2 hours for nice view crossing the Bosphorus Bridge. They leave airport about every 30 minutes at cost about 23YTL flat rate.
If you use common sense there is no need to worry about your personal safety. Be sure to get Liras in the airport ATM's!
Check your bus departure schedule to see what works best for your connection. I prefer Ferry route for a slight time advantage. Either route you take s/b about same money overall. Let me know if you need anything else?
davcamphttp://www.go2istanbul.info/go2istanbul ... ut_Me.html