Baker City is a great place to start any number of road trips that take you off of the interstate. If you are wanting to head toward the southwest (or southeast or further south) the easiest way is to head out toward Sumpter to Prairie City to John Day using Highway 7 to Highway 26. From John Day you can either head further south toward Burns, the Alvord Desert or Hart Mountain using Highway 395, or if you want to keep heading southwesterly, Highway 26 will take you toward Bend where you can connect with Highway 97 that takes you south toward Crater Lake and Klamath Falls. Additional highways from Bend then also can take you further west toward the coastal range an coastal highways depending on your preferred route.
Keep in mind that in winter months these roads may experience unfavorable conditions, although these early months have proven to be fairly mild. Visit the ODOT TripCheck website to keep apprised of changing conditions as you plan your travels. Have a safe journey!