World Values Survey would be a place to start:

http://www.worldvaluessurvey.org/wvs.jsp

I quote Jonathan Perraton. I think the World Values Survey should give some hints for what you are looking for. There are specific sections dedicated to social and political attitudes of respondents.

http://web.worldbank.org/WBSITE/EXTERNAL/TOPICS/CSO/0,,menuPK:64272791~pagePK:220469~piPK:220475~theSitePK:228717,00.html

Check with these World Bank Civil Society guys

For the US, these might be useful:

Current Population Survey (CPS) has lots of supplements with relevant questions http://www.census.gov/cps/

American Community Survey http://www.census.gov/acs/www/

Pew Research has a number of interesting sources:

http://www.pewresearch.org/topics/

Try perhaps the World Values Survey.

Concerning Europe: The Eurobarometer includes questions on trust in various institutions including voluntary organisations/civil society. I think that earlier waves also asked about the preferred provider of e.g. care for older people (welfare state, civil society, families etc.). It may also be worth having a look at European Social Survey or SHARE.

The best dataset is ICCS 2009 of IEA. It is free: http://rms.iea-dpc.org

I'm not sure if I understood the question right. But have you heard about the Social Progress Index? It considers basic human needs, foundations of wellbeing, and opportunities as a complementary but independent measure of economic indicators, such as GDP.

https://www.socialprogress.org/about-us