I have a good friend (not a lawyer) who was born and raised in Chicago who had never heard of Kent.
To give you a feel for how those of us not in the application process are not as familiar with all the schools, today I was ranking law journals. I'm writing an article and am ranking journals so I can figure out where I'm going to submit my article. Conventional wisdom is that the rank of the law review is the rank of the school and the rank of the specialty journal is the school's rank plus 25 or 30. I had a list from Washington & Lee of all legal journals. I had USNews ranking. I was really surprised at how some of the schools were ranked and I'm in law school.
As for the question about familiarity with UNLV, since it's a state school with good sports teams most people will be familiar with the university. There's a general assumption that most big universities have law schools. I think there's also the general presumption that the really bad law schools are private schools and that the state schools are at least 'acceptable.' In a lot of places the private school is for people who can't get into the state school because who in their right mind would give up in-state tuition? Plus people always understand why students chose state schools. For example, I was really surprised to discover that Maine law school was in the 4th tier. I just assumed that since it was a state school that it was at least 2nd tier. Look at how many state schools are in the second tier. Then look at how many private schools are in the 3rd and 4th tiers.
About placement out of state, I would say that it would not be impossible to find a CA job coming from either ASU or UNLV. It will be difficult and you'll have to do a lot more leg work but it's possible. It's also more likely that you won't have a job until you're licensed. As I've written before non top 14 grads overwhelmingly get jobs with small or mid-sized firms through networking. From my experience, it's a lot easier to network when your school has a decent number of alums. Coming from either ASU or UNLV you'll have to make your own contacts. You'll have to go the informational interview route and join the local bar association and perhaps attend some functions.