I'm looking for some feedback or best practice is on how I can take some data with exact locations of events and obfuscate the locations for public consumption in a web map.
I'm only aware of using the Near tool where it can find the X Y of the closest street segments, then display the X Y event data. Effectively moving all incidents to the closest street.
Any other ways to hide locations?
For points, in an edit session, move (translate), rotate and scale by known amounts so that you can unravel back to the original locations.
This is best done with projected data of course
If you don't need the data to be accessible as a Feature Service, you could create a map image layer that displays the data with offsets.
Add the move effect to your symbols and enable symbol property connections.
Have your X and Y offsets defined by the expression (random()-0.5)*50 or whatever distance seems reasonable to you.
Here's a screenshot of a points layer being offset by that expression. Original points in small black, randomly moved points in red.
I've aggregated point features into hexagons or other polygon shapes to still show general distribution of features on a map. If I needed the attributes, I turned them into a table and removed sensitive fields like names. Then in my dashboard, I could still make charts for age, gender, etc.