Head straight to the Old City and start with a visit to the City Palace, Jagdish Temple, and the clock tower area, where you can then have some lunch and explore the winding and hilly streets teeming with shops selling clothing, silver jewelry, and leather-bound journals made with handmade paper. In the afternoon, take a boat ride on Lake Pichola, stopping to explore the Jag Mandir Island Palace. Then wind down your day with an evening sound and light show back at the City Palace. Finish your day with dinner at the legendary Taj Lake Palace hotel (make reservations). Alternatively, take your boat ride in the evening, when the sun begins to set.
You can cram these activities into one very full day, but you should really spend at least two days in this glorious city, especially if you want to also fit in a trip to the arts-and-crafts village of Shilpgram, see some of Udaipur's art galleries, or check out the views from the Sajjan Garh (aka the Monsoon Palace) or the Neemach Mata temple.