There is a museum in Prague, Chech Republic. Check http://www.muzeumkomunismu.cz/en/

There is a museum of socialist art in Bulgaria.You can download apaper about it and the politics involved at the following link http://www.imre-kertesz-kolleg.uni-jena.de/fileadmin/imre-kertesz-kolleg/Portal/Vukov__Nikolai_Socialist_Art_Sofia/Vukov__Nikolai_The_Museum_of_Socialist_Art_in_Sofia_and_the_Politics_of_Avoidance_Forum_Geschichtskulturen__Bulgaria__Version_1.0__26.11.2012.pdf

or http://www.imre-kertesz-kolleg.uni-jena.de/index.php?id=361

There is a Lenin Museum in Finland. Check http://web.archive.org/web/20060113181141/http://www.tampere.fi/culture/lenin/lenina1.htm

In Greece there is a museum of Democracy. Many of its exhibits are related to communism as communists were imprisoned during the 1970s junta. Check http://www.mouseiodimokratias.gr/english/index.asp

There is also a museum against communism. Check http://www.globalmuseumoncommunism.org/

Plenty of museums in Eastern Germany - and a very lively debate on the merits and demerits of their approach.

Just to quote a few:

Stasi Museum - Berlin http://www.stasimuseum.de/en/enindex.htm

Stasi Prison - Berlin http://www.stiftung-hsh.de/

Stasi Prison - Bautzen https://www.stsg.de/cms/bautzen/startseite

DDR Museum - Berlin http://www.ddr-museum.de/

Zeitgeschichtliches Forum - Leipzig http://www.hdg.de/leipzig/ausstellungen/dauerausstellung/

Very controversially, new sections on post-1945 prisoners in former Nazi death camps, e.g. in Buchenwald - http://www.buchenwald.de/612/

You can find a lot of academic critical discussion of these themes in the German language, for instance:

Ruge (2005) http://books.google.it/books/about/Der_Kommunismus_im_Museum.html?id=A6vaAAAAMAAJ&redir_esc=y

Zuendorf (2009) http://www.zeithistorische-forschungen.de/Portals/_ZF/documents/pdf/Zuendorf_2009.pdf

Sabrow (2009) http://books.google.it/books?id=unmp468mnccC&printsec=frontcover&hl=it&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

If you are ever in Vientiane, Laos, check out the National Lao Museum.

http://www.lonelyplanet.com/laos/vientiane/sights/museums-galleries/lao-national-museum

Dear Timothy, it must be extremely interesting...

About 10 years ago I noticed that a 'Museum of Communism' had opened in Prague. However, this is merely memory and I have no documentary reference.

Dear Rob,

Thank you for the hint

Best regards,

Alexandra

maybe you are interested in the approach in Romania  - here is a PhD thesis of Simina Badica. She is the one who wrote most extensively on the theme, as far as I know, amongst Romanian researchers.

https://www.academia.edu/9482288/Curating_Communism._A_Comparative_History_of_Museological_Practices_in_Post-War_1946-1958_and_Post-Communist_Romania_doctoral_dissertation_CEU_2014_

Dear Artus,

Thank you for the suggestion. I did not know about these museums.

Best regards

Alexandra

There is a small, private museum dedicated to the "communist consumer" in Timisoara (Muzeul Consumatorului Comunist) 

http://www.timisoara-info.ro/ro/cultura/muzee/363-muzeul-consumatorului-comunist-.html