Assuming you want your visualizations to be available on the internet, there are many options for this:
It really comes down to exactly what you want to do and how much control you want to have over the map. Additionally you should consider what sort of interactivity you need.
Google Maps is probably the most user friendly for very basic map functions but is somewhat limited in what you can do stylistically.
Mapbox and CartoDB are both user friendly and offer good options for styling and displaying different varieties of data. However, they also both tend to require subscription fees for anything other than small maps. Also, the last time I checked, CartoDB explicitly handles animation and time-series data where Mapbox does not.
D3 will probably give you the most control over display, animation, and interactivity but also has a long learning curve. Even if you don't want the map to be available on the internet, this is still a very good tool for making interactive visualizations that run in the browser.
If you don't care as much about the visualizations being online, you can get a lot of work done in open GIS software like QGIS or GrassGIS, though I don't know if user interactivity is really an option there.
As I said though, it really comes down to the specifics of exactly what you're trying to do and how comfortable you are with various aspects of mapping and coding.
