As far as the islands go, IMO, Oahu is like a city, Kauai is like a small town, Big Island is like the country, and Maui is like the suburbs. Weather is ideal year round on Hawaii, with certain sides of each island being rainier and windier than the other side.
If you want an active night life and tons of activities/restaurants, go to Oahu. There are tons of affordable places to stay, esp on the north shore, but you’ll want to stay on Waikiki if you’re looking for action. Waikiki comes alive at night and has a constant urban buzz about it. The other islands tend to go to sleep or slip into low gear once the sun sets. (The sun rises and sets early in Hawaii.) Car rental isn’t a necessity on Oahu as you can get to plenty of places via the bus. And you can rent a car on a daily basis via rental places in hotels. (Hilton Hawaiian Village has one, for instance.)
If you’re a nature lover and love hiking, snorkeling, and just cold chilling, head to Kauai. This is the least developed of the four island I mentioned, so there’s not a ton of touristy things to do, but there’s plenty of affordable lodging and awesome scenery. It’s very laid back. You have to rent a car on Kauai.
Big Island offers one big thing that the others do not and that’s an active volcano. It also has plenty of lodging, from huge resorts such as the Hilton Waikola to a tree house that you can rent. But it’s big (hence the name) and you’ll be driving plenty if you’re intent on hitting areas of interest. I’ve never been so I can’t offer much advice. As you can imagine, you have to rent a car here.
I personally prefer Maui the best because it’s a hybrid between Oahu and Kauai. It has a small “downtown” with bars and restaurants and shopping, but it’s nightlife is pale in comparison to Oahu. It’s small enough to traverse in one day if you were so inclined, but large enough that you never run out of things to do. It has good snorkeling, good surfing for beginners, a 10,000 foot high mountain, a bohemian town, and a good sprinkling of touristy things such as ziplining (book early), ATV rides, golfing, horseback riding, and sunset cocktail sails.
Maui is also the only island where you can take affordable day trips to other smaller islands (Molokai and Lanai) via a ferry. If I had one week to stay, I’d make Maui my destination. If I had longer, I’d first spend two or three days on Oahu to check out the USS Arizona, Fishbowl Cemetery, and Mighty Mo and the nightlife of Waikiki, then I’d head off to Maui for five or more days.
I wouldn’t go to more than two islands because you’ll waste almost a whole day of your vacation getting to the other island and waiting to check in. (Check-out is usually 10 or 11am and check-in is usually around 3 or 4pm.) If you’re on a budget, weekly (5 days or more) car rentals are usually far more affordable than daily rentals. Also, note that some airlines will fly you into one island and out of another for the same price.
There are tons of ways to make Hawaii more affordable. First and foremost is your lodging. Booking mountain view will save you tons of money over ocean front. Booking one of the many specials (e.g. Hyatt’s Pay for 3 nights, get one free) wlll save you money. Call directly and ask for AAA and/or Entertainment rates even if you don’t have a card. (If the deal is great, you can get the card later.)
If you are content to stay someplace other than a hotel resort, there are literally thousands of private rentals on VRBO.com. However, these generally only rent by the week. (One place I’ve always wanted to check out on Maui is Maui Kai as those units are very affordable and right on the beach (and I mean literally right on the beach) so the view from your lanai is remarkable. The hotel pool is meh as it sits behind the building, but at $200 a night, what do you want?
You might also consider renting a timeshare. There are two very nice timeshares on Maui (Marriott Maui Ocean Resort and Westin Kaanapali Ocean Resort Villas) and plenty of owners rent out their units out on Redweek.com, Tug2.com, MyResortNetwork.com and/or VRBO.com. (Don’t worry, since you’re renting from an owner, you won’t need to attend a timeshare presentation.) Timeshares offer a great hybrid between a hotel resort and a condo community. You’ll have a kitchenette and washer/dryer, plus an on-site restaurant and great pool. The Westin also offers a free shuttle to Whalers Village and Lahaina (“downtown”) so that you don’t have to worry about drinking and driving.
Another way to save money is on food. Book a hotel that includes breakfast and you’ll save $50/day. Pack a soft sided cooler and stop at the grocery for a loaf of bread, some lunch meat, chips and soft drinks and you’re set for lunch. If you rent a condo or timeshare, you’ll have full kitchens and grills, too. We tend to eat in for breakfast and most lunches and then get dressed up and go out to dinner.
I’ve found the best car rental deals at Alamo via Costco and you tend to get a nice break at 5 days. Go to their site and click through for their codes.
Have fun on your trip! Hope this helps.