Brazos sounds like a wanna-be baller and 100% ******nozzle.
So if P-Bros isn't a high-end eatery, please provide us a list of places that you frequent that are.
Dress code at places like Pappas Bros. is less of a rule and more of a level of respect - for the establishment, its clientele, your date and yourself. There are patrons that remember a time when wearing jeans to just about any night out was unheard of - they are the smooth elders who are in a jacket (and probably a tie), not because they have to but because they want to. They want to show their lady or fellow diners that they care enough to dress up for them. They want to show the proprietors that they respect what they are trying to do. They also have pride in themselves and their appearance.
Dressing like a slob because you can just shows you don't get it. If the maitre d', waiter, manager, sommelier, bartender, etc. look down upon you, they have a right to - because you have shown them no respect.
To the OP - slacks and a button down is minimally acceptable, jacket is preferred. Kudos for asking.