Visit the Mahakaleshwar Temple, one of the twelve Jyotirlingas in India. This temple is dedicated to Lord Shiva and is one of the most revered shrines in Hinduism. You can also witness the Bhasma Aarti, one of the major attractions of this temple, which takes place early in the morning. Afterward, head to the Mangalnath Temple, which is considered as the birthplace of Mars according to Hindu mythology. In the evening, visit Kal Bhairav Temple, dedicated to Lord Shiva's fierce form, Bhairav.
If you're lucky enough to visit Ujjain during Kumbh Mela, it is a must-visit. Kumbh Mela is a religious festival that takes place every 12 years in Ujjain, attracting millions of pilgrims from all over India and abroad. Take a dip in the holy Shipra river and attend the various religious ceremonies that take place during this festival. If you're visiting outside of the Kumbh Mela period, head to the Chintaman Ganesh Temple, dedicated to Lord Ganesha and located on the banks of the Shipra river. In the evening, visit Ram Ghat, a famous spot for aarti and a popular place for devotees to take a dip in the holy river.
If you have time, do visit the Vedh Shala Observatory, one of the oldest observatories in India built in the 17th century. You could also go on a food tour of Ujjain and explore the local street food scene. If you're interested in history and archaeology, visit the Vikram Kirti Mandir Museum, which houses a vast collection of artifacts and sculptures from ancient India. If you have an extra day, consider taking a day trip to the nearby city of Indore, which is famous for its street food and architecture.