If you're hoping to avoid long queues and enjoy a quieter visit, weekdays are generally the best time to see the Taj Mahal. From my experience and based on what many travelers recommend, Monday, Tuesday, and Thursday are usually less crowded than weekends and public holidays. Fridays are not an option because the Taj Mahal is closed to visitors for regular prayers.
The day you choose is important, but your arrival time matters even more. If you're booking a Delhi to Agra one day tour, try to leave Delhi before dawn so you can reach the Taj Mahal around sunrise. This combination of an early morning visit on a weekday gives you the best chance to explore the monument before large tour groups arrive.
Traveling during the off-season, such as the hotter summer months, can also mean fewer visitors, although you'll need to be prepared for higher temperatures. With a little planning, you can enjoy a much more peaceful experience, capture better photographs, and take in the beauty of the Taj Mahal without feeling rushed by the crowds.