If I own a restaurant and bar that has live music as well as Karaoke; do I have to pay royalties to the original artists of the songs?

Yes, depending on the type of services you own and how much.  You should contact the U.S. Copyright Office about the companies with whom you may have such business.  The live music may not require royalties if they are not being reproduced -- usually live performances are exempt.  However, karoake is not necessarily exempt from it -- usually the suppliers involved may include the royalty cost as part of a set package.

For instance, with satellite radio, you pay a set rate on a monthly basis.