ForecastFox does what I need. It works fairly well, supports multiple locations, and does have a bit of flexibility in how you can configure it.
It comes "out of the box" set up for New York City. Since I live in South Florida, that doesn't work for me.
Since I also have quite a few years of programming, I can fix that.
The nice thing is that "fixing" that isn't that tough.
They give you a helpful search box that sets everything up for you. Type in your US Zip Code and it will find your city. The defaults work nicely, but the address for the radar doesn't work for me. Radar doesn't change with the city so you end up looking at the temperature and conditions for "your area" and the radar for the Northeast US.
Not so helpful.
Also it makes a small radar display which, while it works, we can do better.
First, install Forecast Fox. I'm going to assume that you know how, since it's one of the more popular updates to Firefox or Chrome.
It should put a web page up before you telling you that it will update your information immediately.
If it didn't, hover over the current conditions and right click on them for the pop up. Select "options" and the web page will open.
In the locations box, type in your zip code and hit enter. It will create a basic profile for that location. You can then hover over the other profile for New York, NY and Remove or Rename the extra one.
If you want multiple locations, tick the box and it will switch through them every minute or more.
The bit I need to change is the Toolbar Display. Since the radar sites are not linked, I go through the same steps every time I do this.
First, in another window or tab, I surf to www.wunderground.com. It will try to detect your location, if it doesn't search for your zip code or city name.
The radar display on the page has a link on it if you hover over top. Select "NEXRAD" radar. Zoom in and out until you get just the view you want. Click on the "Animate" link to make the radar move. On the bottom left of that display you will find a link that says "View/Save This Image", click on the link.
The result is that you will now have a browser page that will show the view you just had. It will be animated, and there will be no extra bits like ads or controls to move it.
Copy the address of the picture by right clicking on the image and selecting "Copy Link Location" from the pop up.
That picture and the url are what you want. But you can do better...
Go back to your Forecastfox Weather configuration page and find the Toolbar Display section. In the Radar (Or Satellite) box, select Custom. Click inside the URL box and do the following keystrokes:
Why did I do that? Because, Radar. More specifically, I have a large screen and would like to use it. Now when I hover over that little green radar icon in my status bar at the bottom of my browser, I get a big picture instead of a little one.
You can also turn on some of the other weather data, and change the number of days displayed. Mine is 5 days and 2 text labels.
The end result is this oversized picture that is below.