One of your first stops should be Abrahams Well International Visitors Center. Here, you'll be able to find your bearings and get some great tips before you start exploring.
You'll be spoiled for sightseeing choice when in Beersheba. Abraham's Well International Visitors' Center is an ideal place to begin here, but there are plenty of other fine spots to discover. Tel Beer Sheva National Park, BIG Beer Sheva Shopping Mall, and Bedouin Market are not far from the tourist information center and and will cap off your day nicely.