The morning is the best time to visit the Red Fort, which is a UNESCO World Heritage Site. Situated in Old Delhi, it showcases the Mughal-era architecture and art. Afternoon and evening can be spent exploring the nearby markets such as Chandni Chowk and Meena Bazaar, where you can shop for traditional Indian handicrafts, street food and clothes.
The second day can start with a visit to Qutub Minar, which is the tallest brick minaret in the world. It is a UNESCO World Heritage Site and a must-visit for history buffs. Afternoon can be spent at the Lotus Temple, which is a beautiful architectural marvel, and is open to people of all religions. The evening can be spent at Hauz Khas Village, which is a popular spot for the youth of Delhi, and is known for its nightlife, street art, and cafes.
If you have more time, you can also visit Humayun's Tomb, Jama Masjid, India Gate, and Akshardham Temple. A side trip to Agra to see the Taj Mahal is also recommended. To maximize your fun, you can take a food walk tour, go on a cycle tour of Old Delhi, or take a hot air balloon ride over the city.