Watch prices don't vary a whole lot in my experience, which is admittedly limited to Geneva. There, I've only dealt with one JLC retailer, Les Ambassadeurs (you can check www.jaeger-lecoultre.com for the complete list). They had a good selection and were pleasant and helpful.

Wherever you shop, just tell them that the watch is for export and they'll deduct the VAT (which is the only tax applicable) and tell you how to deal with the paperwork.

I wouldn't try to negotiate on price. There are a lot of people buying timepieces (even very high-end ones) who don't bat an eye at the prices, so there's no need for the retailers to make concessions.

You can of course get watches (even apparently new ones) for quite a bit less in the US than you'd pay in Switzerland, particularly through some internet retailers, but these frequently aren't authorized dealers and as a result don't offer manufacturer's warranties. The quality of the product may be just fine, but that's anyone's guess.