Here are the completed sentences with explanations:

1. **The** Tower of London is on **the** North side of the Thames.
- **Explanation:** "The" is used because it specifies a particular well-known location, and "the" is used again for the defined North side of the Thames.

2. He had visited a number of places including **the** USA, **the** Middle East, and **Asia**.
- **Explanation:** "The" is used for "USA" and "Middle East" as these are specific regions. "Asia" does not require "the" because it's a general term for the continent.

3. **The** University of Cambridge is one of **the** most famous in **the** United Kingdom if not in **Europe**.
- **Explanation:** "The" is used to specify the notable university and the United Kingdom. "Europe" does not require "the" as it's mentioned in a broader context.

4. He took **a** job with **the** government because he’s interested in politics.
- **Explanation:** "A" is used for a non-specific job. "The" is used with "government" because it refers to a specific governing body, likely the one associated with his country.

5. New Year celebrations are held in **the** Trafalgar Square in **the** London and in **the** Time Square in **New York**.
- **Explanation:** "The" is used for "Trafalgar Square" and "Time Square" as they are specific places. "London" is used without "the" because it is not a defined feature.

6. The time I spent in France was one of **the** best times in my life.
- **Explanation:** "The" is used to specify the particular time that was significant.

7. After six months in **the** hospital, my grandmother is coming **home**.
- **Explanation:** "The" is used because it refers to a specific hospital where she was treated.

Here is the completed text:

1. The Tower of London is on the North side of the Thames.
2. He had visited a number of places including the USA, the Middle East, and Asia.
3. The University of Cambridge is one of the most famous in the United Kingdom if not in Europe.
4. He took a job with the government because he’s interested in politics.
5. New Year celebrations are held in the Trafalgar Square in London and in the Time Square in New York.
6. The time I spent in France was one of the best times in my life.
7. After six months in the hospital, my grandmother is coming home.