Does a "stopped" EC2 instance cost any money?

There is no charge for a stopped EC2 instance or any data transfer fees.
Associated Elastic IP (EIP) addresses and attached Amazon Elastic Block Store (EBS) volumes will incur charges.

If you don't need Elastic IP addresses, disassociate and release.

As an EBS snapshot is relatively cheaper than an active EBS volume, create a snapshot of the EBS volume, detach the volume and delete it. In future, you can recreate the EBS volume from the EBS snapshot and attach it back to the instance.