You can make a great loop between Portland and John Day. The most exciting route will be to take Highway 26 all the way. It will take you over Mt Hood into central Oregon and through The Painted Hills. Total driving time is about 5 hours.
For a return trip, I recommend heading north through The John Day Fossil Beds on OR 19 to Arlington. There you will join Interstate 84 and make the riveting drive along the Columbia River and through the Columbia River Gorge. Driving time is about the same.
I think this is the most scenic tour that will offer up several slices of Oregon for you, though there are other variations. You will find lots of small towns and amenities along the way, which you can check out via traveloregon.com. You can also request printed travel guides.
Enjoy your trip!