Tornado Alley is in Michigan and Wisconsin in July. Maybe northern Indiana and Illinois. Lived in SE Michigan 25 years, Central Florida two years, Oklahoma 33 years and communities I was in were all hit by tornadoes in the time I was there. I've actually seen them only in Michigan and Florida; in Oklahoma and Kansas we don't go outside to watch during tornado warnings. The whole country between the Rockies and Appalachians is Tornado Alley, the belt moves north and south with seasons. The area you are probably worried about usually sees no wet storms from July to mid-September. High winds, yes, all across the plains, Dakotas to the Rio Grande.
Best route is I-94 to Chicago, then the Route 66 diagonal toward Los Angeles: I-55, I-44, I-40, I-15. Your severe thunderstorm/tornado risks in July will be across Michigan, then down through Illinois and Missouri.
If you don't want to see the Great Plains, or have seen enough of them, you can work your way down to New Orleans (I-57 or I-55 out of Chicago) and across I-10.
At any point going south on those you could take I-20 west, it mergres with I-10 in west Texas.
If you take I-57 out of Chicago area, you can pick up I-40 west to Little Rock, I-30 into Texas, where it merges with I-20 and in turn I-10. I-10 thus gets very busy, as nearly half the traffic from the eastern US bound for Souther California gets funneled into the I-10 corridor, while the rest follows the Route 66 corridor.
The east-west Interstate highways further north I-70, I-80, I-90 are bound for northern California or the Pacific Northwest, with a lack of decent diagonals west of the Mississippi. Indeed, only three N-S trunk Interstates to take you south from a northern route (35, 25 and 15) and one of those starts east of the Mississippi and crosses it.
You could drive up to the UP of Michigan, and across US Highway 2, but that's no guaranteeing storm avoidance. I've been in tornadoes in Marquette and in northern Wisconsin in July. 35 years of summer trips between Oklahoma and Detroit, I've learned to watch the weather forecasts, see where the storm systems will be, and adjust my route daily to stay behind the system, or go around them, or sit them out for the night.
Routes I actually use southern Michigan to my corner of Oklahoma include I-80 to I-35 down through Kansas City; I-80 to I-57 to I-74 to US-36 to I-35. I-69 to Us-24 to I-57 then same as the previous. For a long time it was I-69 to I-70 to I-44, but that one goes through both Indianapolis and St Louis and is most likely for bad weather in July-August.
Winter routes, I've gone as far south as Nashville, then across I-40 and back north, but that's tricky because a managable snowstorm in the Great Lakes and upper Midwest might be ice in the mid-South. Not that it matters for July, just showing this trip has many possible variations to deal with weather.
Summer storm cycle is usually about 6-15 days, systems move at 15-30 mph, are a width such that they clear in 2-4 hours if you stay in one spot. Difficulty for travel is that they spread out on a SW-NE front, e.g. El Paso can be in the same front as Chicago and storms slide towards the NE along the front. Thus if you're following that diagoinal, particularly eastbound, you can stay in the same system for 2-3 days. Thus my adjustments to route or schedule try to stay behind the storm. If westbound, you may be clear for several days to more than a week, once you get past or wait it out to pass you.
