Lots of good advice above, I'll add mine. Yes, spend part of your time on the north coast (it's actually somewhat isolated). Do the (easy part) of the Na Pali coast hike - turn around at the beach, it's a spectacular hike, not really difficult (gets muddy in places, though). Yes, the parking for the trail-head fills up, get there early or be prepared to hunt for a legal parking spot. Also spend some of your time on the east/south - we liked Poipu, despite its somewhat high-end/developed feel. We weren't crazy about the more populated eastern coast, but there are certainly more budget-friendly options there. You will want a car to get the best of the island. All of the islands are somewhat expensive, Kauai seems a bit more so than the others. There's a Costco in Lihue, take advantage of it if you want to stretch your budget (we bought half our meals there, one way or another) - of course, it helps if you are staying someplace with some kitchen facilities - we found condos were great for us (as a solo traveler, maybe not so simple to make that work for your budget, but consider it). Yes also to the recommended guide book - that one is awesome. Helicopter tour? Oh yes. A big expense, but it's really the only way to get a good view of the best parts of the Na Pali coast. Jack Harter Helicopters is the outfit to go with - they have helicopters with no doors, so there's nothing but air (and your harness, of course) between you and the world below - makes for glare-free photos and an experience you'll never forget. We did the Na Pali boat trip also; that was just so-so, and did not compare at all to the helicopter views (neither did the price). The boat was just OK. By all means, do make the drive all the way out to the west end and Polihale state park - really wonderful beaches (strong surf, it'll kick your butt but is safe as long as you're paying attention). The so-called "Grand Canyon of the Pacific" (out towards the west end) is worth seeing, though doesn't really live up to the name. Note: Kauai is the northernmost of the (easily visited) Hawaiian Islands. It's cooler that the others and it rains a LOT more there - expect rain often and you won't be disappointed.
Kauai is awesome, I love the place.