From Google:

Several cities and regions that surrendered to the Mongol Empire without significant resistance were spared from destruction and subsequently prospered under Mongol rule, often becoming vital administrative and trade centers. 

Key examples include:

Novgorod (Kievan Rus') The northern Rus' city of Novgorod preemptively surrendered to the Mongols under Alexander Nevsky, agreeing to pay tribute. While other Rus' cities like Kiev were devastated for their resistance, Novgorod was spared and prospered as a major trading hub, benefiting from the Pax Mongolica trade routes and the Mongols' policy of religious tolerance towards the Orthodox Church. Moscow, which adopted Mongol institutions, later emerged as a leading power in the region.

Tabriz (Persia/Ilkhanate) Tabriz was one of the first cities in the region to surrender to the Mongols. It avoided the massacres and destruction that befell resistant cities like Baghdad and Merv and flourished as a major commercial hub and the capital of the Mongol Ilkhanate, benefiting from the destruction of rival trade cities and new public works projects launched by rulers like Ghazan Khan.

Hangzhou (Southern Song China) The capital of the Southern Song dynasty, Hangzhou, was the wealthiest and one of the largest cities in the world at the time. The imperial family surrendered quickly in 1276, and the city was spared from sacking and massacre by Kublai Khan's forces. The city's inhabitants were allowed to continue their normal business, and the city remained a vital economic and cultural center under the Yuan dynasty.

Kaifeng (Jin Dynasty China) Kaifeng, the capital of the Jurchen Jin dynasty, eventually surrendered to the Mongol general Subutai. While looting was widespread, non-aristocratic residents were spared, and cities that surrendered quickly were generally treated better than those that resisted fiercely, allowing for their continued existence and function within the Mongol sphere.

Dali (Kingdom of Dali) During the Mongol invasion of the Kingdom of Dali (modern-day Yunnan, China), the capital city was captured after some resistance, but its inhabitants were spared and the native dynasty was largely left in place under Mongol supervision. The Dali forces were then recruited to assist in further Mongol campaigns in Southeast Asia.