Is it kind of depressing to realize that every big name place you go in your life is getting more shrunk from the expansion of the universe?

No.  This world and all it contains is transitory.  100 years ago, people clamored around certain places and certain people, vehemently claiming them to be great.  But today, most are long forgotten; turned to dust.  The same will happen to the places/people we have today.  In 100 years they won't even be a memory.  That's why I place my treasure and hope with my Father in heaven - where it will never fade away.