The iconic Mysore Palace is a must-visit attraction on your first day in Mysore. Built in the early 20th century, the palace is an impressive example of Indo-Saracenic architecture. You can explore the palace's ornate rooms and halls, and marvel at the beautiful artwork, intricate carvings, and stunning stained-glass windows. After your visit, you can grab a bite to eat at one of the nearby cafes, or explore the local markets for souvenirs and handicrafts.
Start your second day with a trip to Chamundi Hill, one of the most sacred places in Mysore. The hill is home to the Chamundeshwari Temple, which is dedicated to the goddess Durga. You can climb the 1000 steps to the top of the hill, or take a bus or car to the summit. The views from the top are breathtaking, and you can see Mysore spread out before you. After your visit to the temple, you can explore the nearby Nandi Statue, or take a walk through the beautiful gardens.
Other places to visit in Mysore include the Mysore Zoo, the Jaganmohan Palace, and the Brindavan Gardens. If you have extra time, consider taking a day trip to nearby Coorg, which is known for its beautiful landscapes, coffee plantations, and wildlife sanctuaries.