Your hotel is conveniently located. Crossing the Discovery Green park, there is a Mediterranean groceries called Phoenicia where you can get pita bread sandwich and good dessert. MKT bar is next to it.
A couple of blog east just passing Hwy 59 is old Chinatown/Asiantown. A number of good Vietnamese restaurants are here: Huynh, Cafe TH, Kim Son.
Take Metro light rail to northern part of Downtown to Theater District. You might want to check out what's on stage. Irma's mexican restaurant in this area is highly recommended.
When you visit Museum District, do take a relax time at Cullen Sculpture Garden (across Museum of Fine Art). It is a little pocket of modernist sculptures. On weekdays local food trucks offer quick lunch option in this garden.
If your cab take I-45 south to your hotel from IAH, when you approaching Downtown (where I-45 crossing I-10), you will see US President head sculptures (google map: American Statesman Park). They are creation of David Adickes. Well, there are more president heads at Adickes' studio at I-10 and Sawyer (next to a Target store). Google Adickes Sculpturworx Studio.
Also, here is a list of top 10 eateries in Houston Downtown (2013). Ignore Goro&Gun.
http://www.houstonpress.com/2013-05-...n-restaurants/
Enjoy Houston!