There is a huge duty free zone about 20-25 mins from the town centre. It consist of a few streets with huge indoors markets crammed full of stalls selling anything and everything.
What to buy: From cheap electronics to crap plastic toys, to bicycles, to designers sports clothes to leather shoes to pirates CDs and DVDs via everything else you can think of!
BEWARE: When travelling out of Tacna, your bus might be stopped at an internal border check point and you may have to pay duty on what you just bought (I guess if they find it and if it's valuable - our two pairs of shoes did not raise any eyebows! LOL)
What to pay: Bargain, always bargain but remember people have to make a living!
You may find lots of clothes made with Lama / Vicuña / Alpaca wool.
What to buy: They are quite warm and it's an excelent buy . Parkas, hats, jackets, scarfs, T shirts, etc. Some handycraft may be also found.
It's a good chance to buy a Tumi ( a ancian Inca cirurgical instrument)
Just pay attention for if they are Peruan or Bolivian...
What to pay: I don't recall the prices exacly but i do remember that it was not expensive.