If you want to work at one of the best startups you have to do more than apply. You should try and pick a strategic place, such as the valley or NYC and attend lots of events there and visit startups. When asked what you're working on you could say just finished working at bla, hacking on this in my spare time but looking to work out here.

So that you're not asking for a job but are signalling that you'd be interested in one. I know people with limited experience being offered jobs at great companies just from these meetings and if they know who you are you've immediately got a far higher chance of getting it.

Luckily it's a good time to apply as there's more of a developer shortage than job shortage in tech. If you're savvy then it's not hard at all. Showing things you've hacked together or a portfolio is more important than ever.

All of this seems like a lot more effort than the normal sending out resumes but it's much better. Also I don't recommend cold calling. Start using Twitter more, follow the founders or people within these startups on Twitter and join in with their conversation, show that you're a meaningful, savvy person. Then you can say "I'm going to be in the Valley, think I could swing by and see what you're working on".