Houston is relatively close to the Gulf Coast of Texas. Like a somewhat quick drive across town (quick to us, we drive everywhere here) gets you to one form of water or another.
Either way, you'll have to head south but the first place you'll find a boardwalk on your drive to the coast is in Kemah.
The Kemah Boardwalk: 20 miles from downtown Houston and right on the water of Galveston Bay, you'll find restaurants, midway games, rides, a hotel and plenty of shopping. Be sure to take a ride on The Boardwalk Beast and make sure if you do, that you don't mind getting a little wet. If it's not a choppy day, the crew has been known to spray passengers with water guns to "simulate" sea spray.
If you venture all the way down into Galveston (about an hour from downtown) you'll find a brand new boardwalk that just opened Memorial Day weekend of this year.
Pleasure Pier: Replacing the historic Flagship Hotel, over the water, it also features midway games, rides, shops, restaurants and an "antique" style photo place. One of the big features as far as dining seems to be Texas' first Bubba Gump Shrimp Co.
And of course, there is always Schlitterbahn waterpark.
(Photos from: Kemah Boardwalk and Pleasure Pier)