There's Alta's Cafe [1] near the Rainey street end of the river. That's just about the only one, however. TBH - since you seem to know the area - what do you think about a coffee stand under the 1st street bridge? [2]
[1] https://www.yelp.com/biz/altas-cafe-austin
[2] https://goo.gl/maps/FALgvtUESnu