Here is a list of summer undergrad/first year grad astronomy internships I'd suggest.
I've included a few contacts.

NASA Goddard Space Flight Center (GSFC)
Catholic U of America (a second way to work at GSFC) - contact Dr. Steve Kraemer at CUA Physics
NASA Ames#
NASA Johnson
Jet Propulsion Lab
Lunar & Planetary Laboratory, Tucson
National Optical Astronomy Observatories (both Kitt Peak and Cerro Tololo) www.noao.edu
Gemini Observatory www.gemini.edu
National Solar Observatory www.nso.edu
Space Telescope Science Institute www.stsci.edu
Arecibo Radio Observatory (Puerto Rico)
National Radio Astronomy Observatory (3 sites: Charlottesville VA, Green Bank WV, Socorro NM)
Center for Astrophysics (based at Harvard)
Naval Research Lab (Washington DC)
McDonald Observatory (Texas) http://www.as.utexas.edu/reu/
Maria Mitchell Observatory (Nantucket)
Lowell Observatory www.lowell.edu
SETI Institute www.seti.org

worth trying:
Fermilab
Joint Institute for Laboratory Astrophysics (Colorado)
Southwest Research Institute

any university with a big astronomy department/program, including but not limited to
*Univ. California at Irvine
*UCLA
*Univ. California at San Diego (UCSD)
Univ. California - other campuses: Berkeley, Santa Cruz, Davis, Riverside etc.
Stanford U.
Caltech
Observatories of Carnegie Institute
Dept. of Terrestrial Magnetism, Carnegie Institute (Washington DC)#
Univ. Washington#
U. Arizona
Arizona State U.#
U. Colorado
Univ. Arkansas, both Fayetteville and Little Rock
Penn State#
Cornell (runs Arecibo)
*UNLV
*Univ. Oregon
*Univ. Toledo
*Univ. Wisconsin
Univ. Wyoming Infrared Observatory
etc.

# = has some astrobiology

Here are some European internships, which are probably easier for those with
an EU/ESO member state/ESA member state passport
European Southern Observatory - Munich, maybe Chile www.eso.org
European Space Agency - mainly Madrid, Nordwijk (near Amsterdam)
Try lots of British (and other) universities/observatories/institutes:
Royal Observatory Edinburgh
Universities
U. Cambridge, Institute of Astronomy
Oxford U
Durham University
Imperial College London
Queen Mary College London
Observatoire de Paris Meudon
Institut d'Astrophysique de Paris (IAP) www.iap.fr
CERN, Geneva
SISSA, Trieste www.sissa.it


* had UL summer student in physics (P) or astronomy (A) (partial list):
A 2006 Chip Davis, Univ. Toledo (later got Master's in astronomy there)
P 2006 Wes Miller, UCSD (later won Fulbright to Hungary)
P 2007 Wes Miller, Oregon (later started PhD there)
A 2007 Blakesley Burkhart, Univ. Wisconsin (later started PhD there)
P 2008 Katie Davis, UC-Irvine (later started PhD at Purdue)
A 2010 Shannon Mackenzie, UCLA
P 2010 Jennifer Wojno, UNLV