With chips like that it's best to follow the manufacturer's design closely, unless you really know what you are doing. Ceramics are generally preferred in that sort of application, they are smaller and more reliable than electrolytics, handle high temperatures better, and often have a lower ESR.
For a detailed explanation on this and other related topics, though probably much more than you may be interested in, you can check the excellent "Input and output capacitor selection" Application Report, from Texas Instruments,
http://www.ti.com/lit/an/slta055/slta055.pdf
You can also check some general advice for troubleshooting circuits with linear regulators of the 78xx family,
Linear regulator (L7805CV) outputting 5.8V
Answering specifically your concerns:
You MUST NOT use BIG ceramic capacitors on input or output. It will do more harm than good due to the very low ESR (Equivalent Series Resistance) of these capacitors. On the contrary, small ceramic capacitors (<1uF) can be added to increase the transient response at high frequencies (>1MHz). This can be of huge importance in high speed designs. However, you should better use those 100nF (0.1uF) ceramic capacitors for decoupling directly the power pins of the high speed IC devices.
Keep the 100nF ceramic output capacitor in your prototype. However, it will probably make no difference, as your Raspberry Pi will have some its own high speed decoupling capacitors.
The LM1084 is available in 3.3V, 5.0V, 12V and adjustable versions. Which one are you using? I am assuming you have the 5.0V fixed version. If so, the recommended capacitors for most of the applications, according to the datasheet (pages 8-9), are:
1) Bulk output (load) capacitor: recommended 10uF (Tantalum) or 47uF (Aluminum electrolytic). You are not allowed to use BIG ceramic capacitors at the output of the LM1084. However, the datasheet explicitly states that "Output capacitance can be increased indefinitely to improve transient response and stability."
So, you are perfectly OK with a bulk 220uF electrolytic capacitor at
the output. In fact, the added capacitance will improve your circuit
under "large" and/or fast changes in the load current (like those generated by a USB hub or a Raspberry Pi board).
2) Bulk input (decoupling) capacitor: recommended 10uF (Tantalum) or 47uF (Aluminum electrolytic). Apparently, you are not allowed to use BIG ceramic capacitors at the input of the LM1084. And I say apparently because the input capacitor ESR has very litte or none impact in the stability of a regulator.
My advice here is twofold:
Keep the 470nF ceramic input capacitor in your prototype. It will help remove input transients and noise. It is low valued (<1uF) and at the input, so it won't create stability issues.
Add a 47uF or bigger Aluminum electrolytic capacitor. If you have a spare one, another 220uF like the one at the output will serve good. If you don't add this bulk capacitor, you regulator may oscillate under heavy loads and/or get damaged.
My personal, ethical choice: I try to avoid Tantalum capacitors, whenever possible, due to the enviromental concerns and conflicts it is creating worldwide, and specially in Congo and other African countries,
http://en.wikipedia.org/wiki/Coltan
Best Answer
It doesn't usually matter, but be aware that some linear regulators--the popular LM2940 series, for example--may be unstable if the output capacitor's ESR is too high or too low. As the datasheet for your regulator doesn't seem to say anything about that at a glance, it should be fine with any capacitors you pick, but see the edit below for a warning.
Non-polarized capacitors more than about a microfarad used to be rare and expensive, which is probably why the datasheet shows polarized capacitors being used. Today, you can get 10μF ceramic capacitors for less than $0.30 each.
Edit: As @ThePhoton points out, this regulator may be so old that multi-microfarad ceramic capacitors, with their inherent low ESR, may have been a far-off pipe dream to the engineers writing the datasheet. So this may still be unstable with too low an ESR on its output, so unless you want to test its stability under different operating conditions with the ceramic caps, it may be best to stick to aluminum electrolytics. After all, that's probably what the IC's designers had in mind.