12 days is not a lot when everything is said and done. Lugano itself and its lake deserves some time on its own merit. Lugano is very close to Menaggio on Lake Como. Menaggio is just across the lake from Bellagio and Varenna and ferries are available. Also you can easily drive along the western shore of the Como branch, which is very pretty. The next closest lake is Lake Maggiore (and Lake Orta is also nearby) That deserves a few days. I like Cannobio, but Stresa is also nice and an easy base to visit the small Borromee islands. Orta San Giusto on nearby lake Orta is very beautiful as well. You could drive along the western shore of lake maggiore, hit both Stresa and Cannobio (and Cannero) and return to Lugano via Locarno, or even go back to Zurich via Bellinzona.
Given the limited time you have you may want to reconsider Lake Garda. It's big and beautiful also, but somewhat farther away from the general area where you are, and it might take time away from the rest. Unless you are the type that prefers to rush through things, I would leave lake Garda to another time when you can couple it with the Dolomites and the Veneto region.