Given a string, return a string where every character in the original is doubled
No reason to write anything when string is empty. 

public string RepeatAString(string sInputString, int repeatCount)
{
    StringBuilder sOutputString = new StringBuilder();

    foreach (char c in sInputString)
        sOutputString.Append(new String(c, repeatCount));

    return sOutputString.ToString();
}


I think your solution is the best. Obviously you can use LINQ if you want but IMO it doesn't bring anything to table. 

public string RepeatAString(string input, int count)
{
    return String.Concat(input.Select(c =&gt; new String(c, count)));

}