Tornado Alley is a loose term for the states and regions in the central USA that get tornadoes in the spring and summer with a certain frequency. There is no exact definition of this region but in a paper by Concannon et al. (2000) this map was proposed:
As you can see this includes much of northern Texas, almost all of Oklahoma, Kansas and Nebraska, the Colorado flats and eastern South Dakota. Even portions of New Mexico (east of the Rockies) is included. It is also noteworthy that far eastern OK and Kansas as well as no parts of Missouri are considered Tornado Alley on this map.
This map is a good approximation of where you are likely to end up on a storm chase. There is a very high chance you will be driving towards (or between) storms on Route 83, I-40, Route 35 and I-70 on any given chase week in May. While chasing you are more likely to be on small roads on the country side.
Where you chase in Tornado Alley is very much depending on when you chase. If you chase during peak time of mid April to mid June this is pretty much where you will chase and see tornadoes. Earlier on in the season you will be chasing more to the south and as the jet stream progresses northwards and the moisture reaches further up north you will be more likely to chase in the Northern Plains in June. It is all about probabilities though. There are always outlier storms like a tornado in North Dakota in May or tornadoes in Texas in the summer.
If you are curious to how different parts and states are like to chase in, when you typically chase there and if there are any tours in those states check out the following articles: