Tel Be'er ShevaTel Be'er Sheva is an archaeological site outside Be'er Sheva, with remains from Biblical times (approximately 10th century BC). It is one of the most extensive excavations of a walled city from that period anywhere in the world, and was recognized as a UNESCO world heritage site in 2005.
The site is not very large, and a tour of it will take less than an hour. It is just 5 minutes from Be'er Sheva, just south of Omer, on the way to Tel Sheva. There's a small entrance fee, of about 12 Shekels.
Nabatean RuinsOvdat (Wikipedia entry), located about an hour south of Be'er Sheva on road 40, after Sde Boker, and Mamshit (Wikipedia entry), located about an hour southeast of Be'er Sheva, on the road to Dimona, are two ruins of Nabatean cities. The ruins of Ovdat are more extensive. Both were recognized as UNESCO world heritage sites, and are part of the old Incense and Spice Route from Arabia to the Mediterranean.
Both locations are close to nice hiking trails. The entrance fee is about 20+ shekels.