Where do I record the refund of a registration fee?
If the registration fee refers to a fee expense that you had originally paid but the amount is now being refunded to you, I would credit the same expense account that you had originally charged or debited, and would debit Cash.
If the registration fee refers to an amount you are refunding because someone had originally registered for one of your programs, I would 1) credit Cash for the amount you are paying out as the refund, and 2) debit a contra-revenue account such as Refunds of Registration Fee Revenues. This will allow you to easily track the total amounts of refunds that you make during a year. On the other hand, if it is rare for your organization to refund registration fees, you could simply 1) debit the amount you are refunding to the normal revenue account such as Registration Fee Revenues, and 2) credit Cash.