Invercargill's main industry is meat and aluminium. There's not a lot to do in Invercargill but many of surrounding areas are quite beautifull.
Hitching is easy enough from Invercargill.
Heading West and Through Central Otago
Heading North towards Central Otago (Queenstown, Wanaka etc) or the West Coast (Greymouth, Wesport etc) just take high way 6. High way 6 is the main street through the city, in the south of the city it's called Clyde Street, in the middle of the city it's known as Dee Street and at the north end it's called North Road.