People ride bikes in flagstaff from full rigid 80s mtbs to 50lb DH bikes.
There are smooth trails, rocky trails, freeride trails, and downhill trails.
If you really want to do them "all", I'd suggest a 6" travel bike with a pretty sturdy build. This would give you the necessary machine to go down the odd DH trails, without the weight of an 8-9" DC-equipped DH bike. I use my Turner 6pack in flagstaff with a 6" marzocchi single crown fork. Drivetrain is nothing special, just XT cranks and parts, good disc brakes though for some of the real big descents. At least a 180mm rotor up front is a good idea for this situation. By keeping most of the components reasonable though it is not much of a drag on the flatter trails in flagstaff, and with today's shock-technology you aren't giving up much in pedaling efficiancy either, but you will have a very versatile bike that will be able to handle pretty much anything up there.
It's hard to say if the "middle weight" "trail bike" is going to be as usefull or be the most versatile in flagstaff. I wouldn't want to ride many of the "lightweight" trail bikes such as the intense 5.5, yeti 575 or ellsworth id, in flagstaff. These would do ok on most of the "normal" trails, but the geometry and strength/intended usage is just not enough for some of the stuff that exists up there. On the other hand, the difference between these bikes and a slightly heavier 6" travel bike is not much, maybe 3-5lbs. On the "normal trails" in flagstaff, I wouldn't say that a 5-6" lightweight "trail" bike holds enough advantage over a 4" XC bike (not some stupid race-geometry bike, but a decent 4" travel one) to make a significant difference.
Flagstaff is one of the big reasons I got the turner, so that I have the capability to ride pretty much all of the trails up there, and not really get held back.
Again, there are people that ride rigid single speeds in flagstaff, but you also have some big mountains in flag, some decent vertical, all kinds of trails including ones with drops and jumps, IMO it's nice to have a bike that can decently handle all of it.