Carto: An excellent web mapping platform for spatial data. Has a number of helpful analytical tools (e.g. geocoding). Also interfaces well with various data types, including shapefiles, CSV files, and SQL databases. Carto is a good choice if you want to prioritize the mapped/spatial element of your data.
Datawrapper: "Datawrapper is a tool we built to make it easy for journalists and other content-creators to create simple charts and maps for web articles. To make a chart, you paste in your numbers and choose a chart type. We make sure that the chart you’ll embed in your article at the end is beautiful, responsive and interactive." Datawrapper is an excellent tool for going quickly from data to visualizations. It is free and entirely web-based.
glitch: Glitch is not a "data visualization" tool in the traditional sense. Rather, it is a quirky, colorful platform for coding projects of all kinds. Ideal for artistic and interactive approaches to data visualization. For instance, take a look at the Year in Pixels personal data visualization tool.