Two weeks is enough for one region done properly
With 14 days you can do the Golden Triangle in depth, or one-region South India properly, or Rajasthan thoroughly. What you cannot do is all of the above. Here is the two-week Golden Triangle itinerary I would actually recommend.
Days 1-3: Delhi
Arrive, recover, orient. Old Delhi: Jama Masjid, Chandni Chowk, Red Fort. New Delhi: India Gate, Humayun’s Tomb (genuinely extraordinary, usually less crowded than the Taj). Qutb Minar. Lodi Garden for a quiet afternoon. Eat at Karim’s near the Jama Masjid — been there since 1913, the mutton korma is exceptional.
Days 4-5: Agra
Train from Delhi Hazrat Nizamuddin (2.5 hours on Gatimaan Express). Taj Mahal at sunrise on day 4 — arrive at 6am, the light and crowd situation are both vastly better than midday. Agra Fort in the afternoon. Day 5: Fatehpur Sikri (abandoned Mughal capital, 40km from Agra) then train to Jaipur.
Days 6-9: Jaipur and Amber
Amber Fort (take the road up, not the elephant — ethically and practically better), City Palace, Hawa Mahal. Day trip to Ranthambore for tigers if wildlife interests you — book a jeep safari in advance. Jaipur’s food scene is excellent: dal baati churma, laal maas, and the city’s famous kachoris.
Days 10-14: Jodhpur and Udaipur
Train from Jaipur to Jodhpur (5 hours). Mehrangarh Fort is arguably India’s most impressive — spend a full morning. The blue-painted Brahmin quarter below the fort is best explored on foot in the early morning. Train to Udaipur (4-5 hours). Sunset from Sajjangarh (Monsoon Palace), boat on Lake Pichola, City Palace. Fly home from Udaipur or back to Delhi via IndiGo or Air India.