Sure you can take the same basic plot and set it in a different country, a different era, a place devised from your imagination. There are certain things that will make a difference to the basic story. A land where there are dragons makes the where different and the way people act than today's world with planes, cars and television. So when you're writing the story, you need to find ways to bring the reader into the setting you're using.
So we'll continue with the where. The setting or the where is a backdrop but this also hold influence on the characters actions and reactions. Think of the difference between a ballroom and a prison cell. Consider how the characters interact with the setting. What do they see, smell, touch, taste, hear. All the senses make an impact on the characters and also bring the reader into the story. Just remember not to give too much in a long passage of description. That can be boring. You need to choose the elements you want to focus on. You also want to scatter them through out the story.
So consider the where as part of your story and bring your characters into this setting.