I wouldn't worry about the caching, as your app is unlikely to get the same news coverage as the citi bikes program. I think the author misdiagnosed the citi bikes problem. My guess is they just had too few apache processes. If there was just one database table, the database's query cache should have been able to handle this load. His suggestions of cron based caching are likely redundant and overkill. Even if that wasn't enough, PHP's APC would be a better solution.

You need a way to do geospatial queries and likely clustering of the results. PostGIS will work well, and there are kmeans clustering plugins, or you can just do grid based clustering.