If you have pen and paper and a simulator I don't understand why you insist so much in being given a specific capacitor value to start with. You can just sweep reasonable values and see for yourself.
In any case, as it's been said before, you shall start from your specification back into device sizing. You mention 100mA of load current, I assume this is average DC. What type of load will you be driving? Is this a digital load with average DC of 100mA? If so, you will see very large current peaks and the output and you need to define what undershoot is allowed for your application. A simple Cdv/dt calculation would give you the answer. From there, you can calculate your ESR to achieve stability without compromising dynamic large signal response.
There are hundreds of good papers out there discussing this topic, just search in the Texas Instruments website and you'll find more than enough information.
Also, the simulator is there for a reason, it doesn't cost you a thing to play with it a bit... your electricity bill won't go any higher by running some parametric sweeps.