I bought my D5100 a couple of months ago, as my first ever DSLR, and I absolutely love it, kit lens and all. I *wanted* the D7000, but it was just out of my price range.
Yes, the D5100 is a starter DSLR; yes, it has its limitations and yes, people with "real" DSLRs probably point and laugh at me.

But the D5100 is a great camera for the price, *depending* on what you want to do. I will still buy a better camera when I can afford it, whether that's the D7000 or the next thing out there; but that's because I want to do more with my photography; having the D5100 has helped me to see how much more I could do with more practice and a better camera.
But I am VERY happy with my D5100 and am in no rush to trade up anytime soon. My opinion: any DSLR is better than NO DSLR..and in MY opinion, the D5100 is an absolutely awesome intro-level DSLR. Since it sounds like you just want a better than point-and-shoot camera to take pictures as a hobby, I think the D5100 would be a great choice.
Having said that...$625, in my opinion, is a marginal 'deal.' That's somewhere around 25% less than you can buy one new. WHY is she selling it? WHY didn't she "activate" the warranty? Honestly, I'd call Nikon and ask them the warranty question, because that would be a deal breaker for me, at this price. If the warranty wouldn't apply, spend the extra $200 and get a new one that you KNOW has a good warranty. If the warranty would apply, sure, buy the camera and if you can afford it, use the $200 you save off the price of a new one on another lens.