I believe it is approximately 10 to 15 miles depending on exactly where in the Arboretum and cedar park. But I will defer to A1H as I live on the east side.
This was my favorite place to stay when I lived in Fort Worth and traveled to Austin:
http://www.habitatsuites.com/
Its pricey, but if you're staying for awhile the management will negotiate - very nice black man named Donald. I think he's still there. They were friendly with working girls and the suites have private entry. PM me if you have any questions.