Really, there is no one website for good free tattoo designs. The best thing to do is just a big fat google search for "free tattoo designs" or "free tattoo flash" (the artwork used for tattoos is called "flash"). Just see what comes up and work your way from there. Depending on what you have in mind, you might find a lot of decent stuff.
Well, I take that back a little. Deviant art has a boat load of tattoo artwork. But it can be a chore to sift through. But some of it is pretty sweet.
I've used free artwork for my tattoos. Two of my tattoos are exactly as-is the way I found them, the other two I adjusted the art to what I wanted. For me, I had something in mind for what I wanted, and then when I saw the artwork, it went off like a bell in my head. Sometimes you can find exactly what you are looking for.
But if you have an idea of what you want, feel free to check out a tattoo shop and see what they have up on the wall.
My advice would be to find an idea that you want. Print it out and hang it somewhere where you will see it all the time. If you still like looking at it a few months from now, then it's probably okay.
Also, forget about anyone who says "yeah, but you'll regret that when you get old" bullshit. For one thing, after awhile you won't even notice it anymore. It becomes second skin. Second: nothing about your body will look good when you're old, so fuck it.
Here is a couple on my arm. The wolf paw I just found somewhere. I think I found the cat one on deviant art, and then added the swooping lines to it:
I'll spare you pictures of my stomach. This one is a design I took and manipulated to what I wanted. It was actually two different designs at first. This one goes from my waste line to above my belly button (yes, it was extremely painful):
This one is just like I found it. It is on my right hand side ribcage (it hurt a hell of a lot, too, but not as much as the stomach):