Okay, coupla thoughts (and, yes, I dinna read EVERY other post...):
Yes, $4,000 is not a HUGE amount, but it is $4,000 more than zero. So, kudos to you for wanting your dollars to be fruitful and multiply!
Re: Roth IRA -- you can contribute to a Roth IRA up to the limit that you earned (making a lot of assumptions here, mainly that you didn't earn much and that you are not paying taxes). At your age, you will be VERY happy--20+ years from now--if you follow this path. I suggest Vanguard and somthing like their Global Equities fund or my fave standby, Wellington.
If you want to do as your Grandpa said AND invest AND you are somewhat risk averse, I HIGHLY recommend the following:
http://magicformulainvesting.com/book/about_mfi.jsp
I typically recommend against investing in individual stocks, but given that this is "fun" money, you might consider some of the previous suggestions and look for a cheap brokerage account, study up on the Magic Formula book (free at your library), then learn a lil sum'in sum'in 'bout investing.
Heck, if you are REALLY motivated, you could to the Magic Formula in your Roth IRA, but that might be getting a little ahead of yourself.
Above all: congrats once again on your level-headedness.
(Opposite story: I knew a guy in college who was mistakenly given the proceeds of some sort of grant or loan--I forget--he spent his "windfall" on a weekend at the Waldorf; his parents were *very* upset when the funds were recalled and they had to pay the roughly $4,000 bill...)