If you didn't find nice local things in te authentic souqs, you can go to Sharia Omar al-Mukhtar, the main shopping street with lots of shops. When I visited in 2006 there were not many shops with local craft, but we found a African Art Shop. It was an amazing collection of nice and less pretty things. Cupper, leather, jewellery, fur, books, postcards. The shopkeeper was sitting at a small balcony drinking tea or coffee and overlooking the shop.
What to buy: It was the first place where I found postcards in Benghazi. Lots of cupperwork, jewellery and leather bags. Not only Libyan, but from more places of the continent.
All along the road leading from the seafront to the town hall, there are shops under covered arcades selling men, women and children's clothes.
As everyone was so cold, a number of people wanted to stop and buy some warm clothes. There were many jumpers, coats and jackets sold to tourists that day!
What to pay: A woman's winter jacket was around £10 whereas a mean'c coat around £15