First, lets start with Google Maps. To confirm the area, I started at my house, scrolled east on Parmer Lane, and found the field using the satellite view. Here's a link to the site. OK, so that looks like a runway, albeit one in very poor shape. I then went to airnav.com and searched for anything near 78727, but there were no fields, public or private, in the vicinity. That's confirmed my suspicion that the airfield was no longer active.
Google comes to my rescue again, and a search on "north austin airfield" brings me to this page: Abandoned & Little-Known Airfields: Texas - Eastern Austin area. The last entry on the page is a small history of the Austin Executive Airpark, which operated from the late 1950's through the year 2000. I suspect it closed because of the growth in the area; with Dell expanding, it became more profitable for the owners to scrap the field and parcel off the land for development.