If you haven't already bought your Eurail pass, are you sure it makes financial sense for you? I'm guessing that you will mainly be traveling on weekends, so probably most of your trips will be fairly short. I'd think you could still pick up well-price promotional-rate tickets for a lot of shorter train trips next spring. Some destinations might be best by bus, which the Eurail pass probably won't cover, or by budget airline, which it definitely will not cover.
For Florence, you could train to Brussels (closest big-city option), Amsterdam or Frankfurt and fly to Florence or perhaps Pisa. You can check the flight options on skyscanner.com. If I were going to fly to Italy, I'd probably want to spend the entire 8 days there. Otherwise, you're spending a huge amount of your time in transit by comparison to the amount of time you'll have at the destination.
There are many closer places that are worthwhile, but the weather in that part of Europe is not necessarily going to be great during your time period. I'll leave it to folks who've actually been to Europe before the end of April to come up with ideas. Certainly, any major city (Amsterdam and Paris being the first that come to mind) will have a lot of museums and other indoor attractions.
Edited to add: I'm not sure when the flower season peaks; I know it's early, so it probably falls within the period you'll be in Maastricht, though perhaps not during your girlfriend's visit. That's something I'd definitely check out, because this may be only time you're in the Netherlands during the right timeframe.
