I would like an LED that would be "warmer" than the typical phosphor LED, but not warm like incandescent, which is way too far in the other direction. I prefer neutral white lighting if at all possible. However, color temperature is not the only issue. LEDs could remain as "cool" as they are today, yet still benefit from a more balanced spectrum -- high quality 6500K fluorescent tubes for example render color MUCH better than most phosphor LEDs because their spectrum is more balanced, even at the same color temperature.
Essentially what I would find ideal would be something right in between incandescent and current LEDs -- about 4200K color temperature, but with high color rendering. This has already been done in prototypes by using a blue die, with separate red and green phosphor emissions, rather than blue + yellow green.
4500K with fairly high color rendering can also be created by selecting LED bins that have a slight yellow-green tint to them, like Cree WH, and augmenting them with separate red emitters (the result of which is a mixture that is to my eyes noticeably warmer than a 5000K fluorescent tube, yet cooler than a 4100K tube, hence my estimate of 4500K) Adding the red though really makes a difference in that it drastically improves color rendering by filling in a gaping hole in the spectrum. Another point worthy of noting is the drop in efficiency by doing this is almost insignificant (one Red LuxIII LED driven at half strength will correct about 5 Cree's at full power), yet the improvement is highly dramatic.
The weak red output in current LEDs though is something that filtering cannot fix. Filtering can be used to soften LEDs that are excessively blue, but there is a limit. While I find I can get most LEDs to match Cree WH bins, any stronger filtering than that causes the output to look green.