The correct answer is option 2: Krishna. The Krishna River originates near Mahabaleshwar. Mahabaleshwar is a hill station located in the Western Ghats of Maharashtra, India. It is known for its beautiful valleys, breathtaking views, and numerous rivers that originate from this region.

The Godavari River, on the other hand, originates in the state of Maharashtra itself, but it does not originate near Mahabaleshwar. The Kaveri River originates in the state of Karnataka and flows through the states of Tamil Nadu and Puducherry. The Tapi River, also known as the Tapti River, originates in the state of Madhya Pradesh and flows through Gujarat.

The Krishna River, originating near Mahabaleshwar, flows through the states of Maharashtra, Karnataka, and Andhra Pradesh before emptying into the Bay of Bengal. It is one of the longest rivers in India and provides irrigation to a large area, contributing to agriculture and power generation in the region.

In summary, the correct answer is option 2: Krishna, as it is the river that originates near Mahabaleshwar.