I received a check from a new landlord for a tenant allowance. I know that I debit the cash account - but what account do I credit?

Too vague, and you're assuming accounting people know landlord/tenant stuff. First, are you the tenant? Second, what's the allowance for? I even worked for a property management company once, but it doesn't mean I know what you're referring to. Can't tell you what to do with it if I don't know what this "allowance" is for.