I don't know the exact locations but I have seen plenty of good shots taken near KLAS with aicraft taking off toward the afternoon sun so they must be along the south fenceline somewhere.
As for Nellis, the best location is up along Las Vegas Blvd in the vicinity of the Speedway. Park on the Speedway side of LVB and not on the base side. You shouldn't encounter any hassles if you're on the correct side of the street. If they're landing on 21R, you can be right under the base to final turn which allows for really tight shots like THIS or you can let them slide a little further down final and catch them against the mountain backdrop like THIS.
If they're taking off toward the North, move more toward downtown along LVB and you can shoot them just as they clear the fence. Landing from the south, there are spots down on Cheyanne Blvd but I have to tell you it gets pretty rough just south of the base so watch yourself in that area.
Even up along LVB, keep half an eye on your surroundings. There are often some pretty rugged characters hitch-hiking into town out that way. Exactly where they come from, especially in the summer heat, is beyond me but they'll show up.
If you have really long glass, you can move even farther up LVB to where you are looking right down the runways from slightly higher up than the departure end and shoot evening takeoffs with glowing ABs and the city lights beyond!