I'm currently driving across the country. I'm in the city of Rochester, Minnesota. I know I've made it to the west as the conversation in the breakfast room was: "I want my husband to get me a Glock" "Phfft! The Glock is just like an iPhone. Everyone says you should have one because of the name, but really it's a piece of crap! And the recoil is bad."
At least I agree with the locals about the quality of Apple products.
The first time I drove cross-country (east to west), I and my fellow travellers drove north from Iowa to Minnesota. We stayed in St. Paul one night and we also stayed in or near St. Cloud (IIRC) one night (in the latter case camping outside someone's house). I can't remember in what order. We then drove west to South Dakota but took a detour to Walnut Grove to visit the Laura Ingalls Wilder museum. There was something about Walnut Grove (and I don't think it had anything to do with the museum) that made me feel that I had just crossed over into the West -- for me, the first time, as prior to that trip the furthest west I'd been was Niagara Falls. Once we made it into South Dakota it was particularly clear that we were in the West in a way that was certainly not true of Minneapolis and St. Paul, or the places in Iowa we'd stopped in.
Minneapolis-St. Paul doesn't feel Midwestern to me in quite the way that more easterly Great Lakes Rustbelt cities do, but it also doesn't quite seem "West" either. It's tempting to suppose that northwards the Mississippi River is approximately the dividing line between Midwest (not "East") and West, with Minneapolis being sort of an exception.
On that trip, we drove back eastwards eventually but we took a southern route, so it really provided no insight whatsoever into the question.
Many years after that I drove from Chicago to Seattle. This didn't provide much insight into the "where does West begin" issue, as we drove up through Wisconsin (clearly Midwest rather than "West") and then drove on I-94 during the evening through Minneapolis to Dilworth, a northwestern Minnesota town near Fargo. I would say it was obvious the next day, driving through North Dakota, that we were in the West and not the Midwest, if only because North Dakota was so empty.
The following year I drove east from Seattle to New York, this time going through South Dakota. I remember being aware, as I don't think I was on that first trip many years earlier, that eastern South Dakota was not "Western" in the way that western South Dakota clearly was. What I also recall from that trip was the profound sense of reaching some kind of different region once we crossed from Minnesota into Wisconsin (we must have been taking I-90), because the sense of relative emptiness was gone. And I think for the first time I felt an odd commonality between Midwest and East, though I would normally maintain that those are very distinct regions.
Much more recently I drove from the San Francisco Bay Area to eastern Massachusetts. I took I-80 this time, going through Nebraska and Iowa. I would say that once I got into Nebraska from Wyoming I felt as though I'd gone from "clearly West" to some other region that I wouldn't label West or Midwest. Nebraska also mostly had that "emptiness" quality that seemed to be gone by Omaha and certainly by the time I crossed into Iowa.