Lindau Insel is an island connected to the mainland by a causeway. It sits in the Bodensee (Lake Constance). The town itself is a wonderfully preserved historic town, very easy to walk around. Standing on the harbour, one looks directly forward to Switzerland and look to the left to the Alps and the pretty Austrian city of Bregenz. Travel to Bregenz takes 10 minutes by train around the lake or around 20 minutes by boat across the lake (highly recommended).
Further along the German coast of the lake lies Friedrichshafen with the very interesting airship museum and on to the far west of the lake to medaeval Meersburg and majestic Konstanz and the beautiful flower island of Mainau. These areas can all be visited by boat from Lindau harbour.
Train station is Lindau (Bayern) - right on the harbour.
Google map: bit.ly/fRAd2Y