If you want to create your own map tiles in advance and show them using JavaScript library - use TileMill [1] and Leaflet [2]. Both are excellent and very well documented.
To create the whole map on the fly using JavaScript - try mapbox-gl.js [3]. You should be able to pass your location boundaries via mapboxgl.GeoJSONSource (and then you probably don't even need MapBox API key - haven't tried it, though) and style it like this: https://www.mapbox.com/mapbox-gl-styles/styles/bright-v4.jso...
PS. If you decide to host your own tiles - remember that browsers limit the number of connections to each domain. Your map will load much faster if you serve tiles from several different domains, e.g. tiles1.example.com, tiles2.example.com, etc.
To create the whole map on the fly using JavaScript - try mapbox-gl.js [3]. You should be able to pass your location boundaries via mapboxgl.GeoJSONSource (and then you probably don't even need MapBox API key - haven't tried it, though) and style it like this: https://www.mapbox.com/mapbox-gl-styles/styles/bright-v4.jso...
PS. If you decide to host your own tiles - remember that browsers limit the number of connections to each domain. Your map will load much faster if you serve tiles from several different domains, e.g. tiles1.example.com, tiles2.example.com, etc.
[1] TileMill - https://www.mapbox.com/tilemill/
[2] Leaflet - http://leafletjs.com/
[3] MapboxGL - https://www.mapbox.com/mapbox-gl/