How to find out next character alphabetically?

How about:

char first = 'c';
char nextChar = (char)((int) first + 1);

Note that a char will implicitly cast to an int. Here's a simplified solution:

char incrementCharacter(char input)
{
    return (input == 'z'? 'a': (char)(input + 1));
}

Try this:

char letter = 'c';

if (letter == 'z')
    nextChar = 'a';
else if (letter == 'Z')
    nextChar = 'A';

else
    nextChar = (char)(((int)letter) + 1);

This way you have no trouble when the char is the last of the alphabet.