There are a lot of knowledgeable people on here so you may get a reply saying this is possible but nearest I can see is ‘My FlightAware > Manage > Airports’ which then shows map and various info about airport including arrivals and departures but that is far from automatic.
The airports can be bookmarked so just one button press gets you to airport info.
Your best best is going to be setting parameters with the endpoint I have linked below. You can specify a range of departure/arrival times as well as specific departure/arrival airports. It will be the closest to what you are asking for.
Taylor Fischer -
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