Someone is probably depending on you to keep your checking open so they can earn their commission for you opening and funding the account. In that case I think you would want to wait at least 6 months before you cancel.

6 months is about the minimum for credit cards as well IMO. If you close your CC account before 6 months after getting a huge sign-up bonus, don't be surprised if the bank wants their miles back. You may also be setting yourself up to be denied on future credit card offers with that bank.