So you want to spend the day just watching the diversity of Houston walk by (and perhaps make snide comments to those sitting with you)?  Here are a few places to repose in comfort while you enjoy the surroundings:
The Galleria - THE mall in Houston.  Here you'll find upscale mall rats, folks with too much money, the local dressed up for the trip, and of course the out of towners!  There are other malls in Houston, but none of them are even close to the size of the Galleria, nor do many have the broad range of stores.  Sit near the ice rink to see the kids learning to skate or the teens practicing their routines.  Move on down to the food court to see someone in their Prada best snacking on an oversized cookie.  Venture down one of the massive hallways to see a shopping spree in action.  Grab a seat at the Starbucks to enjoy the aroma and watch overstressed shoppers try to take the edge off with a latte.  Oh and you can do some shopping here too!
Memorial Park - If the weather is bearable outside (avoid the summer), then you can grab a blanket and a picnic basket and head down to the largest urban park in Texas.  Covering 1466 acres, you've got an 18 hole golf park along with facilities for just about every outdoor sport you can think of (including Polo).  Most Houstonians come here for the three mile jogging path so you can watch the healthy, fit, and ... going to be fit go past.  Or you could jump into a game of sand volleyball or softball.  There's also a mountain bike trail for you to enjoy.  Its a bit more active then just people watching, but you'll be happy you did.
Downtown/Midtown - In recent years, Houston has made major strides in rejuvenating its downtown.  There are still sections that should be avoided, but the main club strip along the light rail will be hopping.  Just 5 minutes down the road is Midtown - where the younger crowd in Houston goes to hang out for happy hours after working downtown.  Both areas have their hotspots that ebb and flow as the popular crowd finds a new hangout.  After 7pm, you should be able find a few densely packed clubs along with the surrounding dining establishments packed to the gills.  Parking can get a bit expensive, but everyone will be having a great time and that can be contagious.