The Neanderthin diet is easy, really. Just eat what our hunter-gatherer ancestors ate.

So just ask yourself, If I were naked with a sharp stick, could I get/eat this?

Basically, Meat, Fat, Veggies (no beans or corn), Fruit (limited quantities), and Nuts, and a little honey every once in a while.

Any other foods, like beer, coffee, vinegar, dairy, etc. should be tried very carefully and slowly to make sure you don't have any sensitivities to them.

For example, my hubby can eat a little bread and drink a beer occaisionally and be OK, I can't. A little blue cheese dressing every once in a while doesn't bother me, though.
You just have to find what is best for yourself.