Where can I mail a check to if I do not have credit or debit card?

See this link about payment methods that you can use with your Apple ID --> Payment methods that you can use with your Apple ID - Apple Support

I will let you confirm this but I do not think Apple accepts checks for account balance payment anywhere.

We are not Apple but other end users like you. To be sure, you need to contact Apple support, as they will not see your question here.

Apple ID - Official Apple Support