Should I use a struct or a class to represent a Lat/Lng coordinate?

I can’t see any point in having an interface for this, to be honest.

I would just create a struct, but make it immutable – mutable structs are a really bad idea. I’d also use full Latitude and Longitude as the property names. Something like this:

public struct GeoCoordinate
{
    private readonly double latitude;
    private readonly double longitude;

    public double Latitude { get { return latitude; } }
    public double Longitude { get { return longitude; } }

    public GeoCoordinate(double latitude, double longitude)
    {
        this.latitude = latitude;
        this.longitude = longitude;
    }

    public override string ToString()
    {
        return string.Format("{0},{1}", Latitude, Longitude);
    }
}

I’d then also implement IEquatable<GeoCoordinate> and override Equals and GetHashCode, e.g.

public override bool Equals(Object other)
{
    return other is GeoCoordinate && Equals((GeoCoordinate) other);
}

public bool Equals(GeoCoordinate other)
{
    return Latitude == other.Latitude && Longitude == other.Longitude;
}

public override int GetHashCode()
{
    return Latitude.GetHashCode() ^ Longitude.GetHashCode();
}

Note that you need to be aware of the normal dangers of performing equality comparisons on doubles – there’s not much alternative here, but two values which look like they should be equal may not be…

The point about the parameterless constructor is a reasonable one, but I suspect you’ll find it won’t actually bite you.