Greenbrier is best for catfish and the never-ending baskets of hushpuppies. Be sure to go to the old Greenbrier - the one NOT off the interstate but the one about 2 miles north of 565 at the 4 way stop.
Best BBQ is Thomas Pit out on Hwy 72 in Madison. It is perfection with no additional sauce. Not a lot of fancy atmosphere but the best BBQ I've ever had.
Rosie's Cantina is great for Tex Mex - brand new location on University across from Target.
Pauli's has great steaks if you are up for a white table cloth dining experience.
Beauregard's is widely regarded as having the best wings. Try the honey gold over whatever hot rating that you prefer.
Blue Plate Cafe is owned by the same folks as Rosies and is popular and good. It is a meat and three place.
Edo's is wonderful sushi and Japanese restaurant off Madison Blvd across from Wal Mart. Thai Garden is good downtown or in Phuket at Providence for Thai.
Furniture Factory near downtown -- just off I565 is a good local restuarant and has live music and if you like their pieces take one home...
Blue Plate Cafe is only open until about 2pm.
Same type of place down by the courthouse is Wild Rose Cafe but it's also only open until 2. It's a "When the foods gone, I close" type M+3 place.
Po' Boy Factory is also good but I don't think they're open for dinner either.
I didn't mention these because the OP said the had "One night" in Huntsville.
From a previous post of "the 100 Best dishes in Alabama"
"Big Daddy" chicken plate at Tenders!
Deviled eggs at Mullins Drive In
Fettuccine at 801 Franklin
Florentine cookies at Jazz Factory
"German Brown Farmer's Bread" at Ol Heidelberg
Hot wings & habanero sauce at Beauregard's
Lamb at the Chef's Table
Meatloaf at G's Country Kitchen
Steak at Pauli's Bar & Grill
Tea & "sugar water" pitcher at Humphrey's Bar & Grill
Tex-Mex cuisine at Rosie's Cantina
I can only vouch for the Tex-Mex at Rosie's. My fiancee' is a Huntsville native and while I've visited a few times, I've only eaten at Rosie's and Big Bob Gibson's BBQ. Both were damn tasty, but I can't wait to get back and conquer the rest of this list!