Translation:We go to the city, and we take photos in front of the famous buildings.
As Hungarian doesn't have continuous tenses, often the prefixes show the difference between an activity that is in progress and an activity that gets finished. I think this is what applies here too.
I would say "megyünk a városba", if I was, for example, in the car with other people, heading towards the city, and a friend called me and asked me where I am or what I'm doing.
And I'd use "elmegyünk a városba", if I wanted the focus on the result, that is, being in the city. We have to be in the city to be able to take photos there. The importance of going there is the result, not the action itself, so the prefix is used to express this.
I hope this was understandable.