This post is about just that.

How to see Hawaii on $600 or Less.
1. Find yourself on the west coast for work.
Assuming you don't live there already, invent a reason to travel there and have work pay for all of it. Make sure that your trip butts against a long weekend so you don't have to take any extra vacation days to get out to Hawaii. Plan on a five day trip. Promptly forget that it takes a whole day to get there cause it is actually VERY far away from the mainland. How it got to be a state is beyond me, let alone how it was found to begin with.
2. Don't book your flight and assume that Hawaiian Airlines knows what the heck it's doing.
It's an airline right? It works with other airlines. You bought your ticket so it connects with the HA island hopper, why would you ever think that it didn't work? When the HA attendant tells you that you don't have a ticket, don't believe him. Start to cry. Go back to the United desk and they will fix everything so that you aren't "stuck" in Waikiki for the night, racking up and expensive hotel and bar bill. This will save you at least $300.

When you finally get to the Big Island, the car place will assure you that you are going to hit all manner of indigenous species and natives, and that you'll spend your life in auto-jail. This is a lie. The only thing you are in danger of hitting are the thousands of cats that roam the northern parts of the island. In fact, if you are looking for work "Cat Herder" seems like a field full of promise. All it takes is shining a flashlight into the dark to see the tiny reflective eyes staring at you by the hundreds. Creepy.
4. Camp!
Why stay in a hotel when you can sleep on the beach next to the waves you so desperately want to run in to? Camp sites run about $6 a person and can be reserved online via the Hawaii County website. My favorite campground was privately run though, which cut down on the drunk teenagers partying till 2am. The beach was sandy, the waves lapped gently against my tent... *Note: Pitch it farther back next time

Your rental car contract may say "Do not travel on Saddle Road" (the route to Mauna Kea). Ignore it. It's nicely paved now. The actual road up the mountain might be more of an issue. If in doubt of your car's ability, and to save some money on gas, ditch the car and hitch hike the rest of the way up. Locals are friendly enough, and more focused on making it up to the snow fields to slide down on wake boards. Mauna Kea got 16 feet of snow this year, perfect for snow sports where you can avoid hitting the rocks that poke through around the frost line.

Mauna Kea has a great visitor center, and travel to the top is open to anyone with legs or a vehicle. The view from the top is incredible too, not to be missed.
Side roads, overlooks, ancient Japanese graveyards and hidden beaches are also free. Who needs surf lessons when you can visit the southernmost tip of the United States - and jump off! (Not recommended, though I did see someone do it and live.) Volcano National Park is also free on certain national park type holidays. I happened to hit it on MLK day and the park ranger waved us on through. Nice guy...

If you are even remotely curious, the lava fields are another must. The road ends just south of Kapaahu. There you park and are ushered out to a viewing area about two miles from the active flow. As the sun sets you can see the lava glowing on the horizon, poking out in sly red pockets across a barren landscape. This is where your will power will be needed most: Don't try and get any closer. Guided tours of the lava fields take you 2.5 miles out across what used to be a town to the very edge of the bursting molten rock. Close enough to poke with a stick. And it will cost you...

So far this camping thing has been working out well. My last tip is to stick out the stink, no matter how bad it gets. Don't think about crystal clear fresh water and soap carving paths through the grime on your skin. Don't think about having a single layer of deodorant rather than the five that have accumulated. If you do, you'll give in and get a hotel room for the last night. Be strong.
This trip can best be summed up by the phrase "Vacation ADD." We rented a car and took every road, read every sign, stopped at every stand, talked to everyone. Every choice we made was good, though some were more costly than others. Next time I go, I'd like to hike more. Next time... hmmmm. Isn't there a conference in California in May??