Start your trip with a visit to the Lalbagh Botanical Garden. Established in the 18th century, this garden boasts of a variety of flora and fauna, including the famous Lalbagh Rock. You can take a leisurely walk or go for a jog while admiring the beautiful landscape. June is a great time to visit as it's the season of mangoes, and you can taste different varieties of the fruit at the garden's annual mango festival. Don't forget to carry sunscreen and a hat to protect yourself from the sun.
On your second day, head to the Bangalore Palace, which is reminiscent of England's Windsor Castle. The palace was built in the 19th century for the Wodeyar dynasty and is now open to the public. The palace has elegant interiors, with ornate furniture and chandeliers. The grounds around the palace are also worth exploring, with a beautiful rose garden and a ballroom. You can also visit the palace's museum to learn about its history.
On your final day, take a stroll through the Cubbon Park, one of Bangalore's popular green spaces. The park has several walking trails, and you can admire the different species of trees and plants. You can also visit the Government Museum, which has exhibits on natural history and local culture. The park also houses the famous Vidhana Soudha, the seat of the state legislature. The building has a stunning architecture that you can admire from outside.