1) Your research is spot on. The lower tier schools are more regional in nature. If you were going to apply to these schools, make sure you like the industries/positions/locations that recruit at these schools. You can get a taste by browsing their employment statistics report. You can move to other parts of the country, but it is more difficult to find employment opportunities.
2) I think these schools are comparable to Canadian schools, which are also very regional in nature. People’s opinions differ, but out of the schools you’ve listed I feel that Anderson, Johnson, McCombs, Marshall, and Tepper are pretty much equal in national recognition. Stern is more of a national school, but with more emphasis on finance and in the NYC.
3) I think it will be easier to recruit for NYC and LA from McCombs if you are NOT a US citizen. Companies with offices in those areas may recruit on campus and sponsor non-US citizen for visa. From what I hear, companies only recruit at Canadian b-schools only for Canadian offices.