Step 1: Identify the Sabarmati River.
The Sabarmati River originates in the Aravalli Range of Rajasthan, flows through Gujarat, and eventually drains into the Gulf of Khambhat. It is one of the major westward-flowing rivers of India.
Step 2: Identify the city it flows through.
The Sabarmati runs through Ahmedabad, the largest city in Gujarat and a major commercial centre. Mahatma Gandhi's historic Sabarmati Ashram is also situated on its western bank.
Step 3: Eliminate wrong options.
Jamnagar, Surat, and Amreli are other notable Gujarat cities but none are situated on the Sabarmati River.
\[ \boxed{\text{Ahmedabad}} \]