The Southwest is a fishing area with almost no agriculture so it's ideal to try to eat locally caught fish. The country's very small whaling industry is more or less based in Reykjavík and the whales are hunted in Faxaflói, the bay to the north of Reykjanes. There are very few dining options outside the main towns, but the Blue Lagoon see above has a restaurant, and the Northern Light Hotel on the other side of the geothermal plant from the Blue Lagoon also has a restaurant. There are of course several eateries at Keflavík International Airport.
Kaffitár is one of Iceland's main coffee companies, both as a roaster and a chain of cafés. It's based in Keflavík and their factory also has a nice café.
There are four restaurants in Grindavík, notably the Salthusid seafood restaurant.
Reykjavík is of course known for its nightlife, and Keflavík has several good pubs. Apart from that, don't go to Southwest Iceland looking for nightlife.