You can, believe it or not, find an inexpensive hotel that isn’t bad. Plus, don’t get suckered into paying for transit, taxis, etc. Just arrive in Manhattan and walk. Why take a subway if you’re trying to see the city? Sure, you might take a train if you’re leaving Manhattan, but you probably won’t do that on your first trip. So, just get a plane ticket or drive (if you drive, try to get a hotel with parking either included or partially reimbursed). Snag a free map (free transit maps are great for this) and get a feel for each of the neighborhoods by walking.