New answers tagged heatmap
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I'd go with a combination of tools. R sounds like the best fit for your interpolations and raster formatting. As far as web display is concerned, you have options that include a PostGIS/postGreSQL stack for a 'true' web mapping service. D3.js has good mapping tools (including tile support) that may be appropriate if you're trying to just get something out ...
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To summarize my comments above:
When running a spatial analysis tool on geographic lng/lat tabular data follow these steps:
Make sure your data frame is set to GCS WGS 1984
Create your x/y event layer
Export your event layer out to a new layer (to data frame spatial reference)
Re-project your layer to a PCS using the Project tool
Run your spatial analysis ...
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