Q:

Running multiple try statements within each other?

Would this be problematic and run into issues?
Example:
try {
     File Reader fileReader = new FileReader(blah);
     BufferedReader bufferedReader = new BufferedReader(fileReader);

     // while-statement -- extract information from blah

     try {
          File Reader fileReader2 = new FileReader(blah2);
          BufferedReader bufferedReader2 = new BufferedReader(fileReader2);

          // while-statement -- extract information from blah2
         } catch (FileNotFoundException ex) {
             // Display FileNotFound stuff
         } catch (IOException ex) {
             // Display IOException stuff
         }
     } catch (FileNotFoundExcpetion ex) {
         // Display FileNotFound stuff
     } catch (IOException ex) {
        // Display IOException stuff
     }
}

If it is problematic, what other approach should I look to?

A:

Too many try-catch would complicate code and reduce the code readability which will lead to swallowing an exception and its much more worse than performance issues as it can crash your system unexpectedly.
Here is an example of swallowing an exception and its side effects (multiple point of failures like NPE etc.).
public static void main(String[] args) {
  String dataFromFile = null, dataFromDataBase = null;
  try {
    try {
      dataFromFile = readFile();
    } catch (IOException e) {
       // ignore exception
       // String dataFromFile will be set to null
       // as there was an exception
    }
    // imagine many lines of code here
    dataFromDataBase = readDatabase(dataFromFile.getKey());
  } catch (IOException e) {
     // ignore exception
  }

  // imagine many lines of code here
  System.out.println(dataFromFile.replace(" ", ""));
  //imagine many lines of code here
  System.out.println(dataFromDataBase.getKey());
}
private static String readFile() throws IOException {
  // throws ioexception
}
private static String readDatabase(String key) throws IOException {
  // throws ioexception
}

If you are expecting multiple points in a single method that can throw exceptions then club them into one try-catch and handle them appropriately. Again there can be exception to this specific question but you should always try to reduce multiple try-catch in single method.
Unless you are doing something specific with an exception, use single Exception clause to handle all exception and log details or throw it to the caller to handle it in its own specific ways.
try {
     File Reader fileReader = new FileReader(blah);
     BufferedReader bufferedReader = new BufferedReader(fileReader);

     // while-statement -- extract information from blah

     File Reader fileReader2 = new FileReader(blah2);
     BufferedReader bufferedReader2 = new BufferedReader(fileReader2);

     // while-statement -- extract information from blah2

   } catch (Exception ex) {
      // Display Exception stuff details
   }
}

