There are many open source applications and software available for spatial analysis and visualisation of spatial data. Here are two options and their guides that you may consider using if you want an alternative from ArcGIS.
R/Rstudio (Unix, Windows, Mac OS)
QGIS (Unix, Linux, Windows, Mac OS)
Tableau (Windows, MacOS)
Heatmapper: Create your own heat maps at the click of a mouse. Overlay your own image and input your own data to automatically generate the heat map. This tool would be useful for behavioral studies or space ethnography.
Datawrapper: Open source tool helping anyone to create simple, correct and embeddable charts in minutes. It is easy to use, gives you full control and is customisable.
GEPHI: Gephi is the leading visualization and exploration software for all kinds of graphs and networks.
Voyant (word counts, trends): Voyant Tools is a web-based text reading and analysis environment.
TAPoR: TAPoR (Text Analysis Portal for Research) is a platform to discover research tools for studying texts.
DiRT: DiRT (Digital Research Tools) is a directory of tools organized by research activity.
Data Cleaning Tools
OpenRefine (formerly Google Refine) is a powerful open source tool for working with messy data, cleaning it and transforming it from one format into another.
British Library: Cartographic perspectives from BL Map Librarians
National Library Board Spatial Discovery - Explore over 3,000 high resolution copies of maps/plans
Historical Map - Downloadable street maps (from 1954)
One Historical Map - Interactive viewer of historical street maps and geotagged photographs