Drew, you're definitely on point about Austin having an extensive selection of coffee shops! Some personal favorites that come to mind include Mozart's Coffee (which has a beautiful deck on the water) and Flightpath Coffee House in the Hyde Park Neighborhood, with its variety of food, snacks and drinks (including awesome quiche - served with salsa - and a stock of Kinder chocolate treats). 

Once Over Coffee Bar and Cenote are my favorite!

Jo's Hot Coffee Good Food - and outdoor coffee shop next to Hotel San Jose in Soco. It has great people watching anyday of the week, but especially love a lazy saturday.   

I'll second the recommendations of Flightpath Coffee House and Mozart's Coffee, and add recommendations of Teo Espresso, Gelato & Bella Vita and Ruta Maya International Headquarters.

Mozart's Coffee is one of my favorite coffee shops in Austin because it's right on Lake Austin and the views are awesome. It might be a little cold since you're going in winter but it's worth it to check out. Also Halcyon is a good place. It's also a bar and they have make your own s'mores which is cool. Have fun!