I entered India with multiple entry tourist visa, with a stay not more than 90 days at a time. To exit and re-enter India, do I need to return to my home country, or can I travel to any country?
You do not need to go back to your home country before returning to India, although you do need to exit India before the 90 days elapses. Do note that, for nationals of some countries, 60 days have to elapse before re-entry (this from the Consulate in the US):
Q.27. Is there a limit on how many times can I travel to India with my multiple Entry visa?
There is no limit to the total number of times you can travel to India on a multiple Entry visa.
Q.44. Does the gap of two months between two visits apply to all Tourist Visa holders?
The gap of visits of two months between two visits on a Tourist Visa will apply to Nationals of Afghanistan, China, Iran, Pakistan, Iraq, Sudan, foreigners of Pakistan origin and Stateless Origin.