I recommend you consider Leaflet or OpenLayers ..personally, I prefer Leaflet. If you don't have "that many" location points, I'd just convert them into a JSON file or a GeoJSON file and load them all on $(document).ready(). When I say "that many", obviously that threshold is subjective. I consider it to be around 2000 points/features.
If you want it to be searchable, you have some options. But if you want a search-suggest type functionality like you get on Google, etc, you'll be doing a little bit of extra coding.
Now for some bad-ish news: Coming from a Google Maps API background, one thing the open source world still lacks for the most part are great basemaps and/or aerial imagery with world-wide coverage. If you're area of interest is small, you can probably find free data and make these yourself, but that is a different ball of wax. Since you say the user traffic will be low, you could get away with using basemap tiles from OpenStreetMap, and this will probably be done by most leaflet/openlayers examples and demos you find so examples will be easy. But their data quality varies. If you want/need aerial imagery for a map base, your best bet to my knowledge will be MapBox Satellite. You might also consider Bing Maps API, I think they have an aerial layer. Or Here Maps API.
This is obviously an explanation from about 30,000 feet with a few curated web links to get you started. It might sound like a lot, but you can probably accomplish what you want to do with about 500 lines of code or less depending on how fancy you want to get with it.
As an example of what you can do.. I knew a guy who went on a cruise last summer (2019, pre-covid), and he pre-loaded his phone with a very simple Leaflet map, somehow stockpiled some Google satellite tiles directly on his phone, and was able to use his phone in bizarre locations in the Caribbean in offline mode, taking advantage of the browser's GeoLocation API to see where he was from time to time even when he didn't have access to cell service. ....we probably should have done a write up on that because it was a neat project!