As in many things in nuclear physics this ended up being a collaborative effort, and the award should go to Kilburn, Walsh, et. al. But we want to save some of Geoff's t-shirts for the prize of the upcoming 'detectors of the world' contest, so lets award points for the first to have identified a lab:
Micha: 5
Kathy: 3
Matt: 2

A t-shirt for Micha and espresso for everyone!

The correct answers are:
1) Joint Institute for Nuclear Research, Dubna, Rusia
2) Jefferson Lab, US
3) iThemba Labs, South Africa
4) Universidade Federal de Sao Paulo, Brazil
5) Institute of Modern Physics, Lanzhou, China
6) RIBF, Riken, Japan
7) LUNA (Laboratory for Underground Nuclear Astrophysics? LUNA means moon in Spanish!), Italy
8) Holifield Radioactive Ion Beam Facility (HRIBF), Oak Ridge, US
9) Tri University Meson Facility (Triumf), Canada
10) Isolde at Cern, Switzerland
11) Lawrence's first cyclotron (1931)! http://www.aip.org/history/lawrence/first.htm

I got most images and ideas from a publication called "Research Facilities in Nuclear Physics", IUPAP Report 41