These remote and rarely visited small islands (mostly coral atolls) offer superlative ocean, lagoon and beach swimming, dinghy and canoe rides, shopping for local handicrafts (masks and wood carvings) and small, basic accommodations (government rest houses). A great place to relax, they're in Temotu Province (reached primarily by air from Honiara to Santa Cruz Island, which has accommodations).
The provincial capital, Lata, on Santa Cruz, overlooks Graciosa Bay, where Spanish explorer Mendana tried to establish a settlement in 1595 on his second expedition to the Solomons. (The Spaniard died of malaria within a month and the survivors abandoned the area for the Philippines.) A road along the bay from Lata to the site of the Spanish camp passes many small villages and makes an excellent day hike.
These islands aren't for everyone—they're very isolated and primitive—but we really enjoyed our four nights there. 490 mi/790 km southeast of Guadalcanal.