This is not a general legal question, but rather depends on the rules your city has put in place for the license. If you can apply for a license with a P.O. box, etc., then you can--there is no general law stopping you. If the city's ordinances require you to use a physical address for the license, then use the address of your rental room as the application address, but use the P.O. box as your mailing address--there is no requirement that you have the same mailing address as the addresss used for business registration purposes.