Great job overall!
All the Javascript code is in that html page source. The Bootstrap and jQuery you can grab from their sites. I'm using their latest version for this.
All I did was go copy urls from the NOAA site and fetch just the images and data I wanted from them. Their web site is huge so you kind of have to poke around a bit but they have a lot of data you can get there.
I do have a very old version I played with years ago that I think did pinpoint your location on the Radar map. I'll try to find it and take another look at how I did that and if I can I'll add it to this app.
This is an intentionally minimal approach I took and I made it mainly for when I am outdoors hiking, camping, float trips, ect.
I think it demonstrates a simple way to get started on what you're talking about and maybe someone will. NOAA provides great access and detailed documentation for their data and I'd love to see this little app inspire that!