Courthouse shade buys you a few extra minutes before the heat takes over. Limestone and river air make the afternoon feel slower.
Georgetown has enough choices to match your mood. Tejano Cookers BBQ & Catering Co. can be a good pick when you want brisket with a little extra character. Jimmy Vega's Smokehouse works for a classic Texas BBQ tray and a quick counter. The Pit Barbecue is there when ribs and smoked sausage sound like the right move for a longer lunch.
Order small the first time so you can learn the smoke profile. Weekdays are calmer than weekends, especially when events fill the square. A simple plate beats a complicated one here. If you are taking it to the river, wrap it tight and open it only when you are ready to eat.