How to cover the US map with minimum number of 30 mile radius circles?

I wrote an npm package a while back that will help you work with locations on earth.

You can see a jsfiddle I made that makes random points on a circle centered at some location. The code below is pasted from the jsfiddle because SO wants code when you include a fiddle link, but you are better off to go experiment with the fiddle. The function pointAtDistance() implements the Haversine formula.

For the packing, I'd attempt a hexagon formation - make a grid and eliminate those that don't intersect land. As the earth is a sphere, you should probably find the number of degrees longitude closest to the equator that represents your offset so that 30 mile circles still overlap. Then using that angle, the circles further north will overlap more than needed, but at least there won't be gaps, and the structure is easy to reason about.

function pointAtDistance(inputCoords, distance) {
    const result = {}
    const coords = toRadians(inputCoords)
    const sinLat =  Math.sin(coords.latitude)
    const cosLat =  Math.cos(coords.latitude)

    const bearing = Math.random() * TWO_PI
    const theta = distance/EARTH_RADIUS
    const sinBearing = Math.sin(bearing)
    const cosBearing =  Math.cos(bearing)
    const sinTheta = Math.sin(theta)
    const cosTheta =    Math.cos(theta)

    result.latitude = Math.asin(sinLat*cosTheta+cosLat*sinTheta*cosBearing);
    result.longitude = coords.longitude + 
    Math.atan2( sinBearing*sinTheta*cosLat, cosTheta-sinLat*Math.sin(result.latitude )
        );
    result.longitude = ((result.longitude+THREE_PI)%TWO_PI)-Math.PI

    return toDegrees(result)
}