I will be traveling into London Heathrow airport and then connecting and flying out of London City airport. I have about 4 hours.
Any suggestions on the best and fastest way to do this?
To save some money, and if you don't have much luggage, you can take a combination of the tube and the DLR (Docklands Light Railroad). The journey will take about 1:30.
This site will help you plan the best route according to the time you're traveling:
Journey Planner