I'm Italian and I'm aware that Lake Como is super promoted in the English-speaking countries and everybody talks so much about it, overlooking other great lakes like
Lake Maggiore and
Lake Garda. The latter is very famous among the German-speaking countries and basically a German colony
Garda is also the largest lake in Italy and has some great spots to visit. From there, it's also possible to reach through cable car
Mount Baldo and hike there, if you're looking for mountains. It's a great base in my opinion, as it's really close to
Verona, which has also an international airport (Airport Valerio Catullo). The town of
Peschiera del Garda is located on the South-Bank of the lake and it's just one stop away from Verona's main train station. From this town you can reach every town located on the lake through ferry. There are many interesting towns along the lake with cultural and natural attractions. I wrote a post about some of the towns on Lake Garda some time ago,
you can read it here if you're interested (it would take too long to list everything here). The region of Trentino, famous for its mountains, borders with the North-Bank of Garda, so it would be quite easy to reach other mountains.
It would be also interesting to visit the outstanding
glacial lakes in South Tyrol, literally surrounded by mountains and incredible views, but I guess May would be a little bit too early for that? Not that's not possible to make something like that, but Como and Garda surely have milder temperatures in that period.