Port Blair is a part of:

Concept: In India every inhabited place lies within exactly one first-order administrative unit — either a State or a Union Territory, a territory administered directly by the Union Government. A question asking which unit a named town belongs to is settled by locating that town inside a unit’s own territory, which is not the same thing as naming the unit whose administration it hosts.

Applying this to the passage

1. The passage describes an island group lying in the Bay of Bengal between 6° and 14° latitudes and 92° and 94° longitudes, and calls that group a Union Territory.

2. Its closing sentence states that this Union Territory is at present divided into three revenue districts with Port Blair as its capital.

3. A capital does not automatically lie inside the unit it serves — Chandigarh, for instance, is itself a Union Territory while serving as the capital of both Punjab and Haryana — so one more step is needed here.

4. Port Blair lies in South Andaman district, one of the three revenue districts into which the passage says this Union Territory is divided, and the passage names that Union Territory throughout as the Andaman and Nicobar Islands; therefore Port Blair is a part of the Andaman and Nicobar Islands.

Cross-check against the other places named

Result: only the Union Territory described in the passage contains the capital named in the question, so Port Blair is a part of the Andaman and Nicobar Islands.

Note: on 13 September 2024 the Government of India officially renamed the town of Port Blair to Sri Vijaya Puram. This changed the name only — the town remains the capital of the Andaman and Nicobar Islands Union Territory and still lies in South Andaman district.