Step 1: Understanding the Concept:
The question asks to identify the location of the first and oldest oil refinery in India.
Step 2: Detailed Explanation:
\[\begin{array}{rl} \bullet & \text{The first oil refinery in India, and one of the oldest in the world, is the Digboi Refinery.} \\ \bullet & \text{It was commissioned on December 11, 1901.} \\ \bullet & \text{The Digboi refinery is located in the Tinsukia district of Assam. Previously, this area was part of the larger Dibrugarh district. Among the given options, Dibrugarh is the correct geographical locator.} \\ \bullet & \text{Jamnagar has the largest refinery, and Bombay High is a major offshore oilfield, but Digboi is the oldest refinery.} \\ \end{array}\]
Step 3: Final Answer:
The oldest oil refining unit in India is in the Dibrugarh region (specifically, Digboi) of Assam.