Only if your job offer is in the Bay Area. Some of these companies have branches in smaller cities where the cost of living (and consequently pay) is lower.
That'll give you the best idea of your market value. You don't need to take the position, and if the bureaucracy of an enterprise gig isn't your thing, then maybe you shouldn't, but that'll give you the best float test for what it is that you're actually worth, with which you can parlay into knowledge for salary negotiations elsewhere.
Knowing that Oracle would pay you is great for evaluating whether or not it's worth a $30k difference in salary to not have to worry about a business casual dress code, corporate politics and a rigid command structure.
Not knowing the difference in pay, it's harder to evaluate whether or not it's worthwhile.
Many of the old-school Caribbean pirates were in the navy first, after all...
You could walk into Cisco, VMware, EMC, Pivotal, etc. etc. and find yourself working with close to cutting edge tools, hard problems, etc - BUT have a stable salary, perks, training courses, huge amount of corporate resources to lean on and learn with.
Don't rely on your university for advancing your career. I've basically never seen a university career department with good connections or any knowledge of tech at all.
(Also, shameless plug, but we're hiring in NYC: https://angel.co/cafe/jobs)
If you're looking for remote work, you could start with the list of YC companies. Or just go with any young companies whose products or blog posts or people you admire.
It's better to start with the companies you want to work for, and check their own jobs pages (or ask someone who works there), than to start with aggregated job boards, which are really a wasteland.
If you're not in the area, it gets substantially harder. Some random sources.
https://news.ycombinator.com/jobs
AngelList: https://angel.co/jobs
StartupHire: http://www.startuphire.com/