Since you say you will be in Beaumont for most of your visit I will try to mention a few dining options there, etc.
Beaumont is not exactly what one would call a tourist attraction, but I will say it does contain its fair share of good casual dining options with both regional and national chains. While there have been some must try local places over the years, I can't think of any that are still in business at this point. Since you probably already know what to expect from the national chains (Chili's, Cracker Barrel, Olive Garden, etc.) I will mention a few of the regional and regional based options:
For great seafood in a upscale casual dining location try Pappadeaux Seafood Kitchen (this along with several other casual dining and hotel options are located near the intersection of I-10 and Walden Rd on the west side of Beaumont). It is a member of the Houston based Pappas line of restaurants (they have at least half a dozen different brands), the food has a gulf coast, but not exactly cajun flare to it, but be aware the place is popular, the last time I was there driving back from Houston a couple of months ago on a Saturday evening they parking lot was packed and there was a 2 hour wait for a table at 5:30 pm, which is saying something considering how big the place it. (I would guess seating for a couple of hundred)
If you get there and they are packed and you don't want to wait there are a few other options in the area, (if you just had your heart set on seafood and don't mind the much lower quality there is a Joe's Crab Shack at the same exit on the south side of I-10 in the Tinsel Town parking lot), but I would suggest skipping it and trying some of the more regional cuisine next door at Cheddars another Texas based casual dining chain with a bit of an eclectic mix of food.
While in Beuamont you are going to want to stay mostly on the west or northwest parts of the city along I-10 on the west side or Hwy 96 / eastex freeway going to the NW. It is not that the rest of the city is particularly bad, it is just there is not much of interest to see there, industrial areas, etc. This is also where the majority of the dining / shopping / entertainment and hotels are located.
If your interested in Historic sites, about the only one that comes to mind in Beaumont, is Spindletop which was the birth of the oil industry in east texas
http://www.spindletop.org/
As far as Houston goes, it might help to know what part of town you are interested in, the greater Houston area is one of the largest cities by land area in the U.S. and it just keeps growing, being nearly constant cityscape around 80 miles across in.
