I am trying to figure out my route from Greece to Istanbul.
I am wondering if it is cheaper to go hop on a boat to nearby coast of turkey
then take a plane from that location to istanbul or if it is better to go from Athens to
Istanbul.

Second: What are the best places in greece. I am looking into natural wonders and architectural places. I dont fancy resort as I am traveling on a budget.

A lot depends on where you start in Greece - if it was from Athens or Thessaloniki then you just get the train. If it's from one of the islands near Turkey that has a ferry service to Turkey then it MIGHT be better using the ferry and bus. Otherwise all roads lead to Athens by plane or ferry then on from there

Thanks Alan. So, I can take a train from Athens to Istanbul? How long does this take? Do you know the website for the train?

If your goal is to reach Istanbul from Athens without stopping anywhere in Greece along the way the train would be the least-expensive way to do it. But if you plan to visit some islands first then you will save time by making your way into Turkey by ferry and then from your port of entry in Turkey to Istanbul by bus. There are 5 Greek islands from which you can enter Turkey: Lesvos, Chios, Samos, Kos and Rhodes. Which one you choose depends on which Greek islands you visit before that last one.

Train info:
http://www.seat61.com/Turkey2.htm#Turkey%20-%20Greece

Thanks everyone. About how long does it take if I take a bus from whichever port of entry to Istanbul. About how much does it cost? Thanks so much. I really appreciate the help.

I think you'll get the most accurate information as to bus trips in Turkey if you go to www.tripadvisor.com and ask in the Turkey forum.