What lens would I need to take close up pics of a watch?

Like this

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or this

I have a nikon D80 DSLR and I don't want to spend more than 100 bucks. Preferably manual lens but good and sharp!

A macro lens - but your budget is way too low. The cheapest I can recommend that's decent is the Sigma 50mm f2.8 macro.

You can't get a macro lens for $100, but you can get a nice set of extension tubes. Extension tubes allow you to decrease the minimum focusing distance so that you can get closer, and there's no reduction of image quality.

The only downside of tubes is that they don't allow you to focus out to infinity.

This set is cheap at only $80: http://www.bhphotovideo.com/..._Tube.html.

There are better sets out there if you want, but these work well.