I've been to Hawaii 7 times and my personal favorite island is Maui. My advice is to stick to 2 islands, esp if you're trying to get timeshare exchanges, which are often weekly. Which 2 islands you pick is entirely up to you. Generally speaking, Oahu is the most crowded with tons to do and tons of people, Maui and BI are like the suburbs, and Kauai is more rural, with not as much touristy things to do.
Anyway, here's my advice:
1) Decide on what is most important to you: Airfare OR lodging:
If you absolutely must rely on timeshare exchanges, then clearly securing II lodging is the most important. That will probably dictate what islands you visit, in what order you visit them, and what weeks you travel. If that's the case, then put in your searches as early as possible to try and get that nailed down, because you can't book airfare or activities or rental cars until you do. Note that Jan-Apr is high season on the islands, and probably the most difficult to exchange into unless you pick the 1st/2nd week of January. If you can switch to the fall, you'll find a lot more availability.
If renting lodging is an option, then that really opens up your options, and you can be more in control of where and when you go. A few years I divested my timeshares in lieu of RENTING timeshares, and I found that much less stressful when planning vacations. I cut down significantly on my budget by being able to shop airfares and/or securing flights with my travel points. I've also found that traveling on a Tuesday or Wednesday can often cut airfare by a few hundred bucks/points per person, which usually means 3 or 4 extra nights for no additional money.
Once I get my travel dates locked down, then I secure my lodging via Tug Marketplace or Redweek. Booking a unit with a kitchen and washer/dryer allows me to save a few hundred bucks on luggage fees as I'm able to pack much more lightly. With a reasonable budget of $3500 per week for a 2 bdrm, I can usually find exactly what I want.
Once I get my main timeshare/condo booked, then I work on filling in any extra days. For instance, if I'm flying in on a Wednesday, and can't check into my timeshare until Saturday, I book "side" adventures, away from the resort to fill in the extra nights. For instance, on Big Island, I'd book a B&B in Hilo for 3 nights. On Maui, I'd book 3 nights in Hana. On Oahu, I'd book 3 nights on the North Shore. Etc.
Tips:
When booking airfare, note that you can fly into one island and home from another on the same itinerary. No need to return to the island you landed in, though the most CONVENIENT itineraries are most often through Oahu. If the most convenient/cheapest flight is via Oahu, then consider adding 2 nights to see the Pearl Harbor exhibits, which IMO are incredibly worthwhile. PREFERABLY do this at the beginning of your trip so that you begin your trip on a busy note and end it on a relaxing note.
If you want to see the volcano on BI, which is a 2-3 hour drive from the resort area of Kona, don't try to do a day trip. Instead, do yourself a favor and book a B&B for at least 2 nights to give yourself plenty of time. This requires packing warmer clothes (e.g. long pants and rain jackets), but worth it. Also note that there are 2 airports on BI, so take advantage of that by beginning your trip on one side and ending on the other, which means renting your car with pick up from one and drop off in the other. The Hilo side only accommodates intraisland flights, so if BI is your 1st island, fly into Kona and to the next island via Hilo. If it's your 2nd island, then fly into Hilo and home from Kona.