Hi, I have recently been to Rajasthan. And been to Udaipur ,as per the locals informing about the seasons to visit this place till Holi they say it's an amazing time to visit. I could not attend it but seems like the streets and the places floods with Colors and different ethnicities from around the globe.Sounds awesome to be in Udaipur during holi.
You can visit Jaipur for Holi Festival on 21st.
Every year Govt organize Dhulandi festival for foreigners and only for their hotel guests.
Its one of a kind festival with security and no anti social elements. Vrindavan, is not safe if you want to visit during holi, place will be full of anti social etc stuff.