In the morning, visit the Ooty Botanical Gardens, spread over 55 acres, with a variety of flora and fauna. The gardens are well maintained and have a peaceful ambience. Spend time exploring the different sections - the fern house, the Italian garden, and the water lily pond. After lunch, head to the Rose Garden, which is right next to the Botanical Gardens. The Rose Garden has over 2000 varieties of roses and is a visual treat. In the evening, visit the Government Museum, which has a good collection of tribal artifacts, sculptures, and paintings.
Start your day early and head to Doddabetta Peak, the highest point in the Nilgiris. The trek to the peak takes about 2 hours and offers stunning views of the Nilgiri Mountains. Carry some snacks and water along as there are no food stalls on the way. After lunch, head to the Ooty Lake, which is a popular tourist spot. You can go boating or just walk around the lake. In the evening, visit St. Stephen's Church, which is a beautiful colonial-era church with stained glass windows and a serene atmosphere.
Other local attractions you could check out include the Pykara Falls, the Avalanche Lake, and the Sim's Park. If you're interested in tea, you could also visit the tea estates around Ooty. For a side trip, you could visit Coonoor, which is a scenic hill station about an hour's drive from Ooty. To maximize your fun, try the local street food and pick up some handmade chocolates from the local shops.