Where on the AWS Management Console can I see how much money I'm burning per hour with my Amazon EC2 service?
Amazon Web Services > Account > Account Activity
Expand the entry under Amazon Elastic Compute Cloud
That will show the full breakdown of the hours used and the cost to you. Simply divide to find your hourly cost.
If you want to be more granular, you can download your Usage Report:
Amazon Web Services > Account > Usage Reports
Set report granularity to Hours and click 'Download Report'. However, this report does not include the costs.