I hope the reason for your trip to Methodist isn't too bad. If I were coming to Houston from another city, I'd want to hit these places, none of which is far from the medical center:
Van Loc for Vietnamese. It's just south of downtown.
A place for Mexican food. I don't have a "must eat" name, maybe someone else does. You don't say where you're coming from, but I'd go to Pappasito's. Loud but good food in huge portions.
Treebeard's (downtown, lunch on weekdays only) for Cajun food.
Goode Co. Barbeque, west of downtown on Kirby.
At the next level I'd consider:
A place that serves Texas Gulf seafood, like Tony Mandola's Blue Oyster (2 locations) or Goode Co. Seafood.
Another Viet place, or a Chinese restaurant.
None of these is very expensive.
Since you said you're eating all meals out, scan this web page and see what else appeals to you.
re: John Scar
If its (Methodist hosp) the one in the Med Center then you would need to try and get a smoked burger at Guy's on OST. Ask for bbq sauce with the burger. Tuesd-fri is when you can get these.
Frenchy's creole fried chicken on Scott Street near UH is great for creole fried Chicken.
In Midtown for lunch try Cali Sandwich on Travis for Manh Mi's or Vemiccilli.
Also in Midtown is Mai's and Van Loc both on Milam.
Another in Midtown is Breakfast Klub on Travis. I haven't been but it seems to be very popular.
Since you are in Houston why don't you try and give Thelma's a try. The BBQ is great on occasion and the fried catfish is always good. Thelma's is on Live Oak and Lamar just east of Downtown.
re: John Scar
There is a very good restaurant in the medical center called Trevisio. It is on the fancy side and expensive at night. It is the Commoms. It is a large building with a water wall across from Methodist. You can easily ride the light rail to downtown to eat breakfast at the breakfast klub. They have really good Southern soul food. Ruggles in the Rice Village is very good. There is a good Thai place called Nit Noi there as well. The Rice Village is within walking distance.