A few things to consider in planning:
In Udaipur we loved Devi Garh
Raas Devigarh | Luxury Boutique Hotel Devigarh, it is about 30 minutes outside of town, serene, historic, fun, and you feel like you are part of the surrounding village. We chose it over the Aman and never regretted our decision.
At the Oberoi in Agra be sure to request, in advance, a tour of the kitchen. The executive chef gave us the tour and educated us on how Indian cuisine varies across the country.
In Delhi, Bukhara is touristy but a fantastic place to dine. One of the former chefs has opened a restaurant in Sonoma called Delhi Belly (awful name) if you'd like to pay it a visit before your trip. He even will make you a family naaan on request and several Bukhara dishes are on the menu.
The food at the Rumbaugh Palace is some of the best Indian cuisine we have had.