Check-in opens at 12.01 a.m. local time of the departure of the flight; in fact local time of the passenger's first departure. So in your case, if your friend in Nashville does it and you originate in LAS, it would have to happen at 2.01 a.m. in Nashville. OTOH, if someone were going BWI-LAS-LAX, for example, they could check in for both flights at 12.01 Eastern time even though it's 9.01 in LAS.