Where do experimental particle physicists work?

You will usually work at the experiment you're working on. For instance, most experimental particle physicists now will go work on the LHC, so you'll probably live and work there.

 

Just a little addition:

Though most projects using LHC data are 'based' at institutions all around the world: it is possible you may travel to the area that the project you work on is actually being carried out, but it is not always necessary.

 

Research at CERN http://public.web.cern.ch/public/en/Research/Research-en.html

 

Since no one has pointed it out yet, I should mention that lattice QCD is not something an experimental particle physicist typically works with. As far as I'm aware, only theorists do lattice QCD calculations, and they do it wherever they can get a job (usually universities and national labs), since they can work remotely even if they use a particular supercomputer located somewhere else to do the calculations.