I'm with Ivylog and Tommy G on those routes through the middle of Wyoming by Getting up to 80 and Cheyenne. Sinks Canyon is nice, so is the Dubois route. It's all good. These will get you there the fastest. I'm from Montana and although those areas are amazing, it is farther.
So, it depends upon your time frames. You want efficient go with Ivylog and Tommy G's routes. That will also get you the Tetons. Want to see Montana head north and across. But you will need a couple more days to do that way right. There is also the route through Cody and the east entrance. That is beautiful also. You can't go wrong. There are no bad choices here.