Your faculty adviser / scholarship coordinator for things like Rhodes / Marshall / Fulbright / etc.
Your school's financial aid office
Search amongst the financial aid departments at some of the T14 on their websites - they publish lists of outside scholarships to apply for.
(Wish I could just forward you my whole folder of them...)
Yes, you'll have to submit your FAFSA requests again if you have more than 6 schools that you're applying to.
And it's not terribly hard to apply for all the independent / outside scholarships. Once you complete about 10 applications or so, you pretty much end up cutting / pasting / merging essays and such, except for the occasional one that requires an odd or very specific essay. You can do it. Just sit down and knock them out - it's well worth it if you want to avoid loans when you graduate, and it's better than relying completely on the financial aid package of a school. That being said, it's a numbers game, so apply to LOTS and cast a wide net.