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You can see Mount Panderman looming large from the centre of Batu. It is a good hiking and birdwatching area. If an organised hike is of interest you should be able to find a guide at Coban Rondo Waterfall.
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Transport Museum
Opened in 2014 and part of the Jawa Timur Group, it presents the history and development of transportation around the world. It has many classic cars and motorcycles, and replicas of the presidential airplane, Batavia (old Jakarta), "Gangster Town", Broadway, Italy, France, Germany, England, the Buckingham Palace, Las Vegas, Hollywood, and a floating market.
This is probably the single most attractive village in the area and a day or half day spent just wandering here will be time well spent. Don't get cheated, they sell some hot showers as "hot springs". There's also a notable Hindu temple dating from the Majapahit period in the 15th century.
Batu town square
A small park in the middle of Batu town, where locals regularly take walks and idle about. The newly re-worked Alun Alun is adorned with representations of pretty much all of Batu's specialities: apples, strawberries, milk-producing cows, rabbits, etc. as booths, lanterns and statues. There is also a decent-sized Ferris wheel with Rp5,000 entrance fee.