There was quite a thread just a little while ago on interactive public art maps. One that I've always liked is the Association for Public Art's map: https://www.associationforpublicart.org/explore/public-art/#map/all/

In terms of a broader cultural asset map, I've seen a number of people use Esri/ArcGIS tools, if your agency already has a license. Here are two projects that are in process of data collection but are already live:

Chicago Park District Cultural Asset Mapping Project: https://camp-chiparks.hub.arcgis.com/ 

South Jersey Cultural Alliance: https://www.sjca.net/sjcamp/

I am working on the Chicago project, so I can connect you to the folks who created the webpage, if desired.

Best,

Susannah