Western Tennessee is a region of Tennessee.
There are many roads that lead in and out of the region. The to main interstates that come into West Tennessee is I-40 through Nashville, I-155 into Dyersburg from Missouri, and I-40 and I-55 into Memphis from Arkansas and Mississippi, respectively.
The only way plausible way to get around West Tennessee is to drive.
While you're in West Tennessee, or the South in general, you should try sweet tea.
If driving, with the exception of the interstate in most cases, at dusk or night, keep an eye out for deer. West Tennessee has a large population of deer and they will cross the road. Deer are usally the most active between 6-10 p.m. If deer does try to cross while you are driving, aim your car to where the deer is at, not where the animal is going.