From Bodhgaya, we made a short excursion to drive across the wide Niranjara River bed to see Sujata Stupa, the spot where Sujata's village was. The Dhammika book said it was covered by grass but it has been excavated since. It is worth seeing.
Ven. Dhammika mentioned that there are multiple sites that claim to be the spots where Sujata offered rice milk to the Buddha, all of which are recent creations aimed at collecting donations. We went to one of them and would not recommend you to go -- it seems suspect, and seems a focal point for beggers seeking out tourists.
The site can be very quiet (much more so than the Mahabodhi Temple complex, and could be a suitable place for meditation. I am not sure, however, whether it would be safe to do so.
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