Visualizing complex survey data is something of an art. If the data has been collected and aggregated to geographic units (say, counties or states), a choropleth is one option. But if the data aren't so neatly arranged, making visual sense often requires some form of smoothing to represent it on a map.
R, of course, has a number of features and packages to help you, not least the survey package and the various mapping tools. Swmap (short for "survey-weighted maps") is a collection of R scripts that visualize some public data sets, for example this cartogram of transportation share of household spending based on data from the 2012-2013 Consumer Expenditure Survey.
Take a look at the script that created this chart and the other scripts available at swmap to learn some R-based techniques for visualizing survey-based data. And while you're there, browse the rest of asdfree.com for other useful resources (including data sets and tutorials)on analyzing survey data, for free, with R.
Analyze survey data for free: maps and the art of survey-weighted maintenance (via the author, Anthony Damico)