Find your county's groundwater programs
Local health departments can provide helpful guidance on siting and maintaining water-supply wells and often provide a water-testing service if you're concerned about the quality of the water in your domestic well (usually focused on nitrates, bacteria, and, in some counties, arsenic).
Watershed planning groups often evaluate groundwater as part of locally-based water resource management efforts. The website for Wellowner.org has helpful information related to groundwater and private water well systems, including tips on maintaining and testing your domestic well.
Below is a list of links for many of these local programs: