The last decade has seen an increasing number of tourists travelling to visit natural wonder sights, ancient heritages and different cultures around the world.
travel, visit both mean the same and therefore this sentence has lots of redundancy.
While some people might think that this international tourism has negative effects on the destination countries, I would contend that it has contributed to the economic development as well as preserved the culture and environment of the tourist destinations.
This is ok, but better you split it to two sentences - one to discuss the background of the argument and the other to state your personal view on that. It is always better to conclude the introduction with a clear statement that confirms your position on the argument.
Firstly, international tourism promotes many aspects of the destination country's economy in order to serve various demands of tourists.
Your idea does not flow well;
First, international tourism helps boost the host country's economy by creating a demand for accommodation, transportation, food and other logistical requirements.