We no longer subscribe to SurveyMonkey but you may be able to use it for free (with lots of embedded ads).
Here are sources of datasets on a wide variety of subjects.
ARDA: Association of Religion Data Archives - data and GIS maps of religious denominations in the U.S. and worldwide
DataBlog from The Guardian (UK Newspaper) - many data sets and analysis on a wide variety of topics.
GESIS - European and international data
Google Public Data - visualize data analysis.
Pew Research Center - access to data sets available with free registration.
UNC Dataverse / Odum Institute Data Archive - open repository of social science data sets, including state-level polling data