I have two 8-hour layovers in Istanbul. One is during dinner time (5pm-1am) and one is early in the morning (6am-1pm). I've never been and I don't know much about it. Any suggestions for what to do/see on the cheap side? Can I take their train to the center city area from the airport?

Yes, you can take the train from the airport to the Sultanahmet area (or very close to it). For the 5pm-1am shift you could visit the Blue Mosque and go inside to admire the interior. Depending on how long you plan to stay inside the mosque, you might also be able to make your way over to Istiklal Caddesi where the street is more alive with shoppers and tourists in the evening than Sultanahmet.
For 6am-1pm day I think you'll have time to visit inside the Aya Sofya (9am-7pm, daily except Mondays. Get there early to avoid potentially long line. Before that you can just walk around the area.

is it worth leaving the airport and getting a visa and going through customs and everything to check out istanbul? i only have 8 hours...how much of an ordeal is it to leave the airport and come back in the same day for an international flight?

I had two long lay-overs in Istanbul, and it was worth leaving the Airport. The line for the Visa was very short and moved quickly. (cost was $20) A friend and I had never been there and we managed to to do quite a few things considering it was late at night when we arrived. Its easy to find an english speaking taxi cab driver that will take you around the city. We went to a few bars there and they were really cool. They even had a Supper Club. I recommend exchanging currency at the airport there for Turkish Lira, especially if you walk around the main streets located right near the airport. Lots of cute shops.

very helpful nereydag, thanks! any other experiences?

It would be worth it even just to see the Ayasofya.

Hi

How about dinner at the fish restaurants in Kumkapi. Refer this excellent site - http://www.turkeytravelplanner.com/g...sBars/kumkapi/

also, if i take a cab from the airport to the city of istanbul, will it be pretty easy for me to return to the airport? or via the subway system?

thanks again!

I would look into getting a private guide, It may cost a bit but you will see more.

I had an 8 hour lay over in Amsterdam.
I booked a private guide, he was right there when I walked out of the airport.

He took me to all the major places and drove me back to the airport in time.
I had no worries

Percy, I'm on a very strict budget, so I don't think I can afford a guide, but thanks for the suggestion!