If you are staying in self-catering accommodation on Hvar, you'll find two small supermarkets on the main square in Hvar Town, plus a bigger one, Konzum (Dolac bb) near the bus station. There's also a daily open-air market for fruit and vegetables between the bus station and the main square.
The classic gift to bring home from Hvar is dried lavender or lavender oil made from the organically-grown lavender for which the island is renowned. You'll find a row of stalls selling lavender on the palm-lined seafront-promenade in Hvar Town.
Hvar also produces some excellent wines – the best reds coming from the south coast and the best whites from the northern side. If you have a car you might drive out to visit wineries, where you will be able to taste wines before you choose which bottles to buy. Two of the island's top wine makers are Plenković (Sveta Nedjelja; + 385 21 745709; www.zlatanotoc.hr) and Tomić (Jelsa; + 385 21 768160; www.bastijana.hr).
For general information on what to expect of shopping on the Dalmatian Coast, see my Shopping in Dalmatian Coast page.