If you haven t been down to the Green Belt recently (Twin Falls), then you may want to consider that area. The water is flowing and there is actual fall/winter color foliage.Another cool spot is the Zilker tree which should be up and running soon.I hope this helps; Merry Christmas!
I ve got to agree with the other two answerers. The Zilker Tree is great, but I think it s been done a lot. For a good outdoorsy shot with your pup, I would recommend a shot from the Mount Bonnell area overlooking Lake Austin (maybe with the 360 bridge in the background as well). Also, maybe a shot on the Congress Avenue bridge with the capitol building in the background. I love a long shutter time for that location at night (light smears ), but you d probably get a blurry dog.
Despite rumors that it has been canceled this year, the Zilker Tree made of hundreds of colored lights, always makes a nice background. There are several spots in town that would put the whole tree in the background, or if you just wanted to get the lights, you could go right to it. Also, people who live on/around 38th street do some pretty cool features every year. You might want to check that out.
The trail of lights may be a good place to take photos. I have not been there in a while but heard it s a nice place.