Another really excellent steak restaurant is Churrasco's. It's not too far away from downtown, but it will be a cab ride away (the location I've always been to is on Montrose and Westheimer). Their steak is amazing, but they have a lot of other good entrees (as long as you're not eating vegetarian). It's a little on the pricey side, but it's cheaper at lunch and probably still cheaper than London. The rest of their menu is sort of Latin American fusion (so not Tex Mex).
Also, while Houston does not have good public transportation, one thing they do have is a light rail line that runs from downtown to the Houston Medical Center. If I recall correctly, it shouldn't be more than a few blocks from the convention center to the light rail.
The Medical Center itself is not that exciting, but there are some things very close to it that are fun. The Museum District has the Houston Museum of Natural Science, the Museum of Fine Arts Houston (as well as a few other other museums), and the Houston Zoo. All of those are well worth a visit if you have time, and all are within an easy walk of a light rail station.
Rice University is also right near the museum district, and while the campus itself doesn't have much to offer tourists other than being pretty, there is a shopping area called Rice Village just to the south of it. There's a lot of different stores and restaurants there, some part of a chain and some independently owned. It's not right next to the light rail line, but it's not too far a walk from it.
If you get the chance to try a Vietnamese sandwich at any point, by the way, you should totally have one. They are amazing, and one of the things I miss most since moving away from Houston. The restaurant we always go to is called Cali Sandwich (it's in Midtown on Travis, I think), but I'm sure there are other places. But the best thing about Vietnamese sandwiches, other than their general deliciousness, is that they can be as cheap as $3 per sandwich. The least expensive ones are in Midtown (which is just south of Downtown).
As a general thing, Asian food of all varieties tends to be really good in Houston (since there are a lot of immigrants from various countries in Asia who live there).