I'll third the advice of booking accommodation ASAP. You will already be too late for some places.
I have been to Skye many times and personally would never want to do it without a car. Depends on your plans though. I go out walking and need the flexibility.
www.walkhighlands.co.uk is good, both for researching walks/nature and it has some accommodation listings. They also have a very active forum including trip reports. There are plenty of people in Scotland who religiously use public transport. Its possible but you have to plan around it.