In New York, check out airbnb.com or craigslist for private accommodation. I was in NY a couple of years ago and rented a place privately for about 10 days. In LA, I've recently stayed in a private apartment and a cheap hotel, both times in Beverly Hills and both were fine. The hotel was cheaper and less hassle, though not particularly charming - look up Rodeway Inn (I think it was called). Probably US$89+tax? Use priceline.com, hotelbookingpro.com, etc to find deals. Tripadvisor.com can give you a decent indication of what's good, but doesn't cover every single option.
In Vegas, I stayed at the Encore and Palazzo - both are excellent, but book ahead to avoid paying full price (second night at Encore was going to be US$700-800 so we shifted to Palazzo (around US$250). Do the Bellagio buffet for lunch (if you get the offer to eat at the bar, do that to skip the line). The Bank (in Bellagio) was a decent club but look out for ways to skip the line and halve or avoid the cover charge (US$40 a few weeks ago). The cheaper hotels are still absolutely fine so you could go cheap on the accommodation and spend up on food/drink instead.
For car rental, I rented twice with National in August and they were great.
If you want any more info, yell out. The August trip covered LA, San Diego, Phoenix, Seattle, Portland and San Fran (plus various national parks) - though it wasn't basketball season so besides the NBA store in NYC (which you'd already know about), I can't help there.
