Living in the U.S. and being involved in the travel industry, I would first ask where you intend or would like to travel once you reach these shores? Fact is, a lot of people plan to arive in New York City, when their actual destination is elsewhere. There a re lots of flights from London (for example) to Boston, Chicago, Detroit and even Minneapolis (for the mid-western minded) and of course the southeast and west.
The single greatest misconception I see on this and other English and European threads is that the U.S. can be travelled in a short period of time, such s motoring from London to Paris for example. As jno has pointed out numerous times (he's well travelled in the U.S.) the country, from coast to coast is over 2,500 miles in distance. There are huge stretches out west where I live, that take hours if not days to drive across with not much to see once the initial infatuation with high desert and sagebrush is satiated. So keep that in mind when planning your itinerary.
Driving in the U.S., even the large metroplexes is reasonably easy. The Interstate highway system truly is a modern miracle of convenience and safety.
So, after deciding where you'd like to go in the amount of time you have to spend, simpley Google something like "Things to do in Phoenix" for example. You'd be surprised what you'll find that may fit your temperment and interests.
By the way, Welcome to the U.S! You'll find the overwhelming majority of Americans very friendly and quite interested in your accent, asking where in Australia you live...