It is kind of hard to describe the traffic patterns in detail, but I am assuming that you will head north across the river on MoPac and approach UT from the West. Prior to that, though, depending on where you are in 'SW Austin', you might come all the way up MoPac, OR take 290 after the Y in Oakhill to MoPac, OR take Brodie up to 360 and then get on MoPac from 360, OR come through the Y in Oakhill and get on MoPac via 290, OR come up SW Parkway to MoPac. There are also a variety of 'back ways' that might get you over to 360 and then to MoPac and avoid the Y in Oakhill.
I am sure that none of that is helpful, really, sorry

. In short, I much prefer 'inside the Y in Oakhill' (that is where Hwy 71 and 290 split). There are a lot of options inside the Y, but the ones that are further north are generally a quicker commute, and the ones to the West of MoPac have an option of taking 290 or MoPac to get up toward the river.
The neighborhoods off of SW Parkway always look like they are backed up trying to get on MoPac, but I don't really know how bad it actually is, or if there are alternatives.