Breakfast tacos at pretty much any non-chain Mexican restaurants are a must. If you find yourself down south, you've got to get to Valentina's BBQ for breakfast AND lunch. Also, I know it's a bit of a tourist trap now, but I'll never get over the Don Juan taco at Juan in a Million.
As others have said, La Barbeque is just as good to me as Franklin's and a shorter wait. If you're north of downtown I'd reccomend Stiles Switch BBQ.
Not much of a drinker anymore, so can't say much on that front. Rainey Street used to be my area, but that's blown up like the rest of Austin.
And FYI, the Pecan Street Festival is going on this weekend. So all weekend most of 6th Street is going to be filled with crafts and art booths, live music, food, etc. Could make for a good detour is you're willing to handle all the traffic added on to the norm.
Tailgating is spread throughout random parking lots and grassy areas near the stadium. Were always friendly to me in the past and the harshest insults I've gotten are that I'm wearing the wrong shade of orange.