I recently received a job offer from one of the giants in SV for a software engineering role in the bay area (I am not from the US originally). The base salary they gave me is lower than the average of what you see in Glassdoor and the like for a similar position with my experience (about $10k of a difference).
When trying to talk with the recruiter about this I was pretty much told that unless I have another offer in hand (he literally asked to see a contract, is that a common thing to ask?), there's nothing he can do about it.
So I'm basically left with trying to get another offer from a company I don't plan on joining, or accept this offer which I'm not happy with, but from a company I do want to join. Is there a third option that might help me here?
There's very little downside to trying to negotiate your job offer, even without a counter offer on the table. The outcomes are pretty easy to enumerate:
1. You ask for more money. They negotiate; you end up with a higher salary. It might not be what you initially asked for, but that's how negotiation works, and it should be higher than what they offered. This is a success.
2. You ask for more money. They say, "Oh geeze, we're really sorry, but there's straight up no room for negotiation here; you're either going to have to accept the offer as it stands, or walk away". This isn't a success, but it's not really a failure either because you haven't lost anything; you're in the same place you were before, making the same decision, but now you've got a little more information.
3. You ask for more money. The company is offended that you have the temerity to negotiate, and they take their offer off the table. This looks bad, but it's a success as well. If a company gets salty at you for trying to negotiate a better salary and rescinds your offer, that's a pretty clear sign that you wouldn't have been happy working there and you've dodged a pretty major bullet. In my mind, that's good news.
For advice specific to negotiating, even without a counter offer, I'll point you towards Patrick Mackenzie's blog post on the topic; it's got some very good advice and is worth reading: http://www.kalzumeus.com/2012/01/23/salary-negotiation/