To avoid the crowd of tourists at the restaurant, pack a picnic lunch, blanket and swimsuits for a lunch break at one of the lake beaches. You can hike around the lake with your stroller, but sometimes it is a bit rocky. Plan some additional time for the hike.
Lake Eibsee is accessible as a day-trip from Munich; therefore, on the weekend it can be crowded with day-trippers. The lake is less crowded during the week.
Lake Eibsee can be visited throughout the year, although the summer months are nice for a picnic by the lake and for swimming. A word of warning, even in the summer months the water is quite cold.