Expenses, recording and managing.

You would enter any expenses in the same manner based on how they were paid.  For instance, if you paid the hotel bill using the credit card, then you would enter credit card charge and apply the amount of the hotel bill to your hotel expense account.

I have several subaccounts under travel expense account:  automobile mileage, hotel, air fare, etc.

When I pay any expense that should go under travel, I apply this to the appropriate expense account.

I don't use QB to track mileage.  When I pay a mileage reimbursement check, I apply the check amount to my mileage expense account.