Accommodations in Manhattan for budget travellers are hard to find. We stayed at the White House hostel which was an experience. It totally had bed bugs, but maybe if you scoped out your room ahead of time (to make sure it's bed bug free) it would be worth it? Your call. It was definitely the tiniest, sketchiest rooms ever.
We stayed at hostels in L.A. There is a cool internationals-only one of Melrose. I've heard good things about the ones on Hollywood, but my favs were in Venice Beach (I just like being near the ocean though if you stay in Hollywood you can make a day trip of the beaches if you want). I like both Venice Beach Hostel and Venice Beach Cotel. Cotel (I think) is internationals only. Also there's a great hostel in Vegas on Freemont with a pool and a bar and group outings. I had lots of fun there.