Which option does the best fit here?

I would have to go with broaden. I think that this is the best word to use for this type of sentence. Broadening the mind means that the mind will become more open-minded probably because it will be exposed to new sights and sounds.

There are a lot of people who say that after they have started traveling, they realized that the problems that they are going through are usually so small. There are a lot of opportunities that may be waiting for them when they check out different places. Some of them end up falling in love with the position that they have visited that they plan to live there. Others do not want to settle yet and would like to reach all of the ends of the world.