Adair Kitchen on San Felipe & Sage (just outside the Loop (610). If you think that most places have overly sweet pancakes, try their's. They serve lunch and dinner also.
Le Peep off Westheimer on West Lane, just inside the Loop. Kinda hard to find, tucked behind new shopping strip next to River Oaks District. Typical breakfast fare but they have really jacked up the prices.
Drexel House is a wine bar/restaurant serves breakfast also. Behind Crate & Barrel in Highland Village, off Westheimer, before you get to Weslayan (just inside the Loop). Very simple, limited breakfast menu. Not great/not bad. Dinner is hit or miss but good location to sit outside and people watch.
Just down the street is Central Market and they make great breakfast tacos. Get there early. They're usually gone within an hour. They open at 8 am.
A little bit further away but if you get the chance try Snooze; an Austin import on Montrose, just south of Westheimer (Way inside the Loop). The omelettes are great, the pancakes are good. Parking is a pain in the ass.
And if you're a runner, do the 2.8 mile loop in Memorial Park. Afterwards head about a mile east on Memorial to a tiny little restaurant. I think it's called Sunrise but not positive. But it is connected to a Shell station. Great breakfast tacos.