**Explanation:**

The climate of a place is determined by various factors such as geographical location, altitude, proximity to water bodies, and prevailing wind patterns. In the case of the given options, Mussoorie is the place with a cooler climate even during summers.

**Factors determining the climate:**

1. **Geographical Location:** Mussoorie is situated in the foothills of the Himalayas in Uttarakhand, while the other options are located in different regions of India. The proximity to the Himalayas plays a significant role in Mussoorie's cooler climate.

2. **Altitude:** Mussoorie is located at an altitude of around 2,000 meters above sea level. Higher altitudes generally have cooler temperatures due to the decrease in air pressure and the associated drop in temperature.

3. **Proximity to Water Bodies:** Mussoorie is relatively close to the Yamuna River, which acts as a source of moisture and helps in maintaining a cooler climate. Mumbai, on the other hand, is located on the coast of the Arabian Sea, which leads to a relatively warmer and more humid climate.

4. **Prevailing Wind Patterns:** The wind patterns in Mussoorie are influenced by the Himalayas, resulting in cool and refreshing breezes. In contrast, cities like Allahabad, Mumbai, and Amritsar may experience hot and dry winds during summers.

**Conclusion:**

Considering all these factors, Mussoorie has a cooler climate even during summers compared to the other options mentioned. Its geographical location in the foothills of the Himalayas, higher altitude, proximity to a water source, and prevailing wind patterns contribute to its pleasant weather throughout the year.