Stereo panning for piano and drums - how would you pan it ?

I pan drums from the audience perspective.  However, how wide depends on the style of music.  For big rock drums I pan them as wide as I can get.  I usually pan the kick and snare straight up the center and spread the toms right to left.  For jazz, I treat the kit as a whole and keep it a little narrower--including overheads.
 
I don't usually pan a piano across the speakers.  It's usually either to the right or the left (depending on how I envision the "stage").  If there are no other instruments besides the piano I may pan it more center and then use some reverb to widen it a bit.  From the piano players point of view the lower register is on the left and the upper register is on the right but that's not how a piano sounds to someone listening.  So if you're going for a natural--realistic--sound then it's all about how it sounds in the room.
 
My approach to mixing is always from an audience perspective.  It's very rare for an audience to be sitting at the piano or at the drums (or any instrument) and even less likely for a recording.  From the audience's point of view, each individual instrument is a mono sound source that may occupy a different space on the stage.  So, I move things around by panning them and placing them on a "stage" in the stereo field.  When it comes to effects like reverb I decide how big I want the room and pan it appropriately.  I might use some reflections from the opposite stereo side to get a sense of width. Even an orchestra can be thought of like this; ie.  the 1st violins are no the audience left, the cellos are on the right, etc.  But the 1st violins may reflect around the room, same is true for cellos.  This, to me, is where the illusion of "stereo" comes from.
 
This is less true for electronic music.  You can spread synth pads really wide because it's not a natural sound.  You also might have the concept to put the listener in the music and you mix from stage center instead of in the audience.
 
Then again ... you can do anything you want and as long as it sounds good (not necessarily "right" or "correct") then go for it.

I mix drums from the audience perspective but when recording, I give the drum his mix with his perspective.
 
For keys, I am with bit on the player's perspective.
 
Vanblah has good advice on panning as well.  It can be rewarding to note the drum panning in all kinds of different genres of music to see what great producers used.  

It doesn't matter - except for drummers.  And whether they want to play the part or just listen ;-)

For piano, the long held traditional view is that you must pan it from the audience perspective.  Which is a little awkward because the string have a front to back alignment from the audience not left to right.  For the most part however, if you are miking outside the piano with a stereo pair, the mic pointing to the right will be panned right and the one pointing to the left will be panned left.  Truth be told, if you listen to a classical piano album, you will not hear much of the separation between bass and high strings, since the mics are usually placed several feet outside the instrument in a great sounding room.  You just hear the wonderful sonority of the piano in a spacious environment.  
 
Personally, as a piano player, I am also used to the sound of the player perspective, and in pop music, depending on the needs of the mix, bass on the left is perfectly acceptable, and I sometimes prefer it if a wide stereo separation needs to be made.  

I think audience perception can be almost anything depending....so I tend to mix  with enough separation until it sounds good. I don't often think of the, "where they might be sitting if this were real" thing. If I mixed orchestra it would be more critical I suppose.
 
I tend to pan pianos and drums based more on where I want them in the mix which is habitually bass left because I am accustomed to hearing it there. With drums, since I'm not a drummer, I pan toms and cymbals either way. I don't often pan more than  10/20% either way so it sounds good in stereo but you don't loose much if you only hear one side or in mono.
 
Bat has a good point...the combination of mono channels can give a stereo effect at the master, but stereo channels are usually already in stereo and if it was done right it is already ok.

I position the drums from the audience perspective.  Hi Hats on the right side and ride on the left with different sounding crash cymbals on both sides of the kit.
 
I don't know anything about mixing fake drums but when recording live drums I use two mics over the kit.
 
There are several ways to do this but ... the point I want to make is that if you record live such that the overhead mics are picking up the whole kit with the ultimate intention of panning those mics hard left and right ... then, when you bring in the close mics on the individual drums, their positioning (i.e., panning) has to be consistent with their positioning in the stereo field created by the overheard mics.  

well, as far as the overheads go, they capture not only the kit, but the sound of the room.... and the relative placement of the kit in the room... and all those reflections and whatnot are what the really smart part of your brain tells you what a 'direction' is....
 
so if a tom is banging off the side wall of the studio or stage, it is going to sound a certain way to it's own mic, and that also translates to the overheads, and if you mess with that relationship, you are in sonic trouble.
 

dmbaer
For an acoustic recording of a drum kit in a medium size or larger sound stage, the live sound source will sound like a mono source coming from whatever pan position the drum kit occupies on the stage.

A kit has several resonating heads in different locations that can be many feet apart from each other on larger kits and the resonating heads are oriented in different directions (i.e. snare/horizontal and bass drum/vertical).  I can certainly make an argument that the sound of the drums in a live setting are not localized as a single point source. 

If you see a concert at a large venue what you are hearing is the mic'ed (or triggered) drum kit through the PA.
 
If you are listening to an acoustic set of music with a un-mic'ed drum kit in a small venue and you are hearing washed out mono with 80% room sound then the acoustics of the venue suck.

Bass is the easiest for me to make panning decisions on.

Saw an interview with a producer that said he pans to the Audience perspective, but only after asking the drummer. It's not so important to the audience in general, but if it's going to mess with the drummers enjoyment of hearing their performance,  then go with the drummers perspective. Of course this doesn't matter so much if you are using BFD or something.
 
For Piano with stereo width, if you were to se to one side of the stage or the other, would you not place the bass end nearer the centre, whether be audience perspective or not?

Another thing to consider for your overhead mic set-up is that you have a number of options for mic placement or orientation of the two overheads.  Ultimately, the method of overhead mic’ing will come down to your recording space (i.e., the room), the style of music and how the drums sit in the mix.
 
You should probably experiment with different set-ups to get a feel for the different results.
 
- XY (coincident pair)
- ORTF 
- AB (spaced pair) 
- MS (mid-side) 
- Recorderman (1 mic overhead and 1 over the shoulder) 
- Gly Johns (1 mic overhead and 1 mic place horizontal on the floor tom side directed at the hihat) 
 
XY, ORTF, AB and MS all capture the room.  Recorderman uses a closer micing technique giving you a dryer sound.  You will have phase issues with ORTF, AB, Recorderman and Gly Johns.  MS requires a mic with a figure 8 pick-up pattern to capture the sides.
 
My preference is an AB mic configuration.  I know I will have to deal with potential phase issues but there is a fair amount of flexibility in how you aim your mic’s and I find that when I pan the tracks hard left and right it gives me a slightly exaggerated sound stage.