Barton Creek is a very nice facility. I have only played the Crenshaw course, which I thought was wonderful.
If you are staying at Barton Creek, it is not too far to Circle C, which is my favorite public course in the area. To that same end, almost all of the City of Austin Munies have some interesting history behind them. So, even if the courses are not outstanding, they are nevertheless interesting.
Weather: will be great.
Course conditions: not sure of the schedule in Austin, but many courses punch the greens in early April. Accordingly, I would suggest asking before making a tee time.
Food/drink/etc.: For BBQ, Salt Lick and County Line are acceptable. But, if you want truly transcendent BBQ, make a trip out east of Austin to either Lockhart (Smitty's, Kreuz's, Black's) or Luling (City Market). Closer in to Austin, I think the mexican food is better than the BBQ. For a mexican breakfast in an institution, Las Manitas on Congress. For a mexican lunch or dinner, hit Maudie's or Guerro's (Austinites will tell you to skip Guerro's, but it is a good scene with good - not great - food). If you go out at night, skip 6th street and go to 4th instead. [P.S. I realize this goes beyond your original inquiry, but I think Austin is the best city in Texas - no I don't live there - so I wanted to give you some suggestions]
Enjoy your trip.