I'll assume that your 240MHz source is far enough from your "inputs stages" that you actually have a transmission line and that is why you are asking about termination. If the connection is short you're dealing with a RLC circuit and your resistor is more about damping than termination (more on how to determine if your line is short or long in this question).
If you are dealing with a transmission line then you want to match your 240MHz source to the line. So I would place a single series resistor at the source. This will serve as your source terminator for any reflections coming back. Now let's say you now have a 50 Ohm line after your resistor, if you split it into two 50 Ohm lines well now you have an impedance mismatch? Instead you can split it into two 100 Ohm lines. This is the recommended approach for "bifurcated lines" in Johnson's high speed digital design book.
If you could handle the voltage loss you could go further and end terminate the line at your "inputs stages" and you should have a nice clean setup.
On the other hand your example uses a clock. If all you need to do is get a clock to multiple locations cleanly there are a number of inexpensive clock buffer chips or oscillators themselves that come with 2,4,x outputs. Sometimes it's just easier to use one of those.