In a week you'll be able to explore Guadalcanal and either Savo or Tulagi. Base yourself in Honiara and spend three days (four if you're a diver) visiting the capital and the historic sites dotted along the northern coast. Then catch a boat to Savo and settle in for a couple of days of relaxation. If you're keen on diving, opt for Tulagi, which features superb wreck dives. Another option, if your budget permits, is to skip Savo and Tulagi in favour of Tavanipupu Private Island Resort – a luxurious yet laid-back hideaway tucked in a sweet eastern corner of Guadalcanal.
With two weeks, you can easily include the Western Province in your itinerary. Start with your one-week itinerary, then hop west to Munda, which offers great diving and snorkelling options and good day tours to some must-see WWII relics. Afterwards, grab a flight or catch a boat to Gizo where three to four days can easily be spent messing around in and on the water. You might also make time for a hike on Kolombangara. Fly back to Honiara the day before your international flight out.
With three weeks, fly to Seghe and devote a few days to Marovo Lagoon, where all sorts of water activities and adventures await. Thanks to fairly reliable inter-island boat services, a trip to Malaita could even be on the cards – fly back to Honiara and catch a boat to Auki and chill out in Langa Langa Lagoon for a couple of days.