We took a Taxi and did our own thing in Istanbul. Don't get caught by the Taxi drivers trying to sell you the 100Euro site seeing trip! Everything is right next to one another (Blue Mosque, Sophia etc) so just pay 15Euro to be dropped off at one of them and walk around. Be aware of people trying to sell tours, goods etc - just say "no thanks" and walk on.
Another Port we did by ourselves. Just took a Taxi to the old City and walked around. This is a Port you HAVE to get off at. It is absolutely amazing. Pay the ticket price to get onto the City wall - it is worth the visit (and the steps!!)