Breakfast Off The Strip
My recs are Egg and I, and Egg Works. 50's Diner Omelet House on E Desert Inn is another good place that has 3- and 6-egg omelets..
9355 W Flamingo Rd Ste 3, Las Vegas, NV 89147
Egg & I
4533 W Sahara Ave Ste 5, Las Vegas, NV 89102
Omelet House & More
3050 E Desert Inn Rd, Las Vegas, NV 89121
Simon at Palms is without a doubt the best you'll find off Strip. Kerry Simon takes classic comfort food and gives it a fun gourmet spin.
And if you can, do Sunday Brunch there. It's a bit pricier, but totally worth it IMHO!
Simon @ Palms Place
4381 W Flamingo, Las Vegas, NV 89103