1.What hotels are close to the castle? We will not have a car.
2. Where is the train station in relation to this?
1. There are a bunch of hotels near the castle. Using google maps enter: Sirmione. Zoom into Sirmione. then in the search box enter: hotels.
You'll have a bunch of names nearby on the map. 2. The closest train station is at Desenzano del Garda.
The train does not run to Sirmione. The two Lago di Garda train stations are at Desenzano del Garda (west side) and Peschiera del Garda (east side). You would have to take a bus, taxi, or ferry from the train to Sirmioni. You can see the ferry schedules here: http://www.navigazionelaghi.it/eng/g_orari.asp