I think Bologna is a clear winner from the standpoint of variety of local day trips possible by train or bus.
To check options for longer trips requiring flights, go to https://www.skyscanner.com/ and enter, in turn, each of your three possible study locations as the point of origin. Then be sure the "Direct flights" box is checked so you see only non-stop flights, hover over the Destination box and click on "Explore everywhere". I don't think all the flights have been loaded for months as far out as March and April 2024, so you might do best to look at October or November of this year. Choose the month you prefer and then click on Search.
You'll get a list of the countries reachable by non-stop flights. Click in a country box to see the cities with non-stop flights. Some flights don't run every day, and there's a difference between having just one flight a day and four or six when you're planning a short trip. You'll have to drill down more to get that level of detail, but this will give you a start.
The reason for focusing on non-stop flights is that the cheapest way to cover long distances in Europe is a flight on a budget airline, and if you need to connect on a budget airline, you are likely to end up paying, in effect, the total fare for the two flights. And the trip may take 5, 6 or 7 hours, not counting having to get to the first airport early.
A quicker look, based on current flight options, can be found on the website https://www.flightsfrom.com/. It produces a list of destinations showing the days the flights run and how many departures there are on a typical day.