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If you're really strapped for cash, the 70-300VR (or Tamron version) is a really nice lens. In broad daylight, it's a phenomenal lens. And for the price, you really can't beat it. I use it with my DX kit (with 16-85) as my traveling set-up, but use it with my FX occasionally as well.
Other than that, your price range goes up fast. Still, what the others have said... either a 80-200 or 70-200 or 300/4 and a tele converter will get you the most focal length for the money.
I have and use the 80-400 occasionally. It was my first "super tele", and it was what I used when I went to Masai Mara. It worked really well during the day, on slower moving targets. If you want speed, it won't deliver, but range it has.