Specifically I'm looking for web mapping applications that include multiple layers and don't look like an ArcGIS clone -- perhaps something that looks like it was designed by a designer rather than a GIS tech :) This is a list of responses from Twitter, many of which do look GIS-y so more suggestions are welcome...
- https://zola.planning.nyc.gov/about#9.72/40.7125/-73.733
- http://www.censushardtocountmaps2020.us/
- http://historiccensus.longislandindexmaps.org/
- http://longislandindexmaps.org/
- http://dvrpc.org/mapping/webmaps
- http://dvrpc.org/webmaps/tod/
- http://jonahadkins.com/
- https://t.co/yVyY9Yyy1i
- https://t.co/18ESdWhAvO
- https://censusreporter.org/profiles/15000US360594141001-block-group-1-nassau-ny/
- http://cosmos.surrey.ca/external/
- https://t.co/Xn4KOkcdsG
- https://owi.usgs.gov/vizlab/hurricane-irma/
- http://geonode.org (not a site, software)
- https://owi.usgs.gov/vizlab/water-use/
- https://t.co/CH8Y9zB8w9
- http://greeninfo.org/
- https://mkeschoolmap.org/map
- https://maps.nyc.gov/then&now/
- See Stamen Design examples
- https://trase.earth/
- https://apps.urban.org/features/debt-interactive-map/
- https://worldview.earthdata.nasa.gov/
- https://medium.com/@cholmes/wfs-3-0-get-excited-yes-8e904fdbcc0
- http://topotopo.io
- https://t.co/nvo7robYxX (list of map references, links ot other maps)