We stayed on the big island in Waikaloa for two weeks and ate at Lighthouse Delicatessan three times. From the outside, it looks like most buildings in Hawi - cultured and well-worn/loved - but the interior is actually quite new and very tastefully furnished and finished. It opened October 2010 and it already has a steady flow of local customers/lucky tourists coming in to enjoy the absolutely amazing gourmet quality and prepared food.
The sandwiches are amazing - my family enjoyed the classic Reuben sandwich - so good!, a homemade meatball sub, and cranberry turkey sandwiches which were all pretty much to die for. Not to mention the warm soft pretzels made with brown sugar dough and honey mustard - a must try; you'll be back. The fresh bread is also delicious and the people who work there are so personable and always ready to chat, tell stories and have a good laugh.
If you're an outdoorsy type, Chris Scelza (I think one of the owners of the Delicatessen) has some good tips on what to do around the island. He's quite the adventurer himself, having ridden down Lion's Back in Moab, Utah a few times on a bike.
All around, a GREAT place. You would be missing out if you didn't make it here at least once. Delicious, gourmet quality food, great service, great people, great atmosphere and now one of my family's go-to restaurants whenever we're on the big island. Sometimes we make special trips to Hawi just to eat there.