Its totally safe. In ujjain you can visit mahakaleshwar and kaal bhairav. Near ujjain there's Mandu, famous for its fort.
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Omakareshwar has one Shiv Jyotirling. On the other side of river, there is 5-6 kilometre long parikrama which goes in a circular manner on the top of a hill. Along the way, you will find many captivating scenes and shiv temples. At the top of the hill is an abandoned fort.