My ideas, in no particular order:
I have an idea for a story where the Doctor becomes interested in a major real-world problem on modern day earth, and sets out to solve it (this could be a famine, a natural disaster, a power struggle etc). His companion tries to warn him that this problem is beyond even him, but he won't listen and keeps meddling and becoming more driven and desperate until something dreadful happens and he realizes the error of his ways.
I also think it would be interesting to see Doctor-lite episode where an alien invasion or suchlike happens on modern day earth and the Doctor won't intervene because it's a fixed point in time. This would be a bit similar to Fires of Pompei, except the modern day setting would dial up the conflict A LOT. The companion would have real trouble understanding how something from their own time can be a fixed point ("surely it hasn't happened yet. How can it be decided?") and be very upset by what was happening, on a personal level, possibly because people they care about are going to get hurt. The action would focus on the companion defying the Doctor and acting alone.
I'd like to see more stories where the Doctor travels to an alien/future world and discovers something really wrong with the society and helps the people overcome their problems or oppressors. We used to see quite a lot of stories like that in the classic series, whereas New Who seems more about fighting alien menaces.
Finally, an episode told partly in flashbacks, featuring a classic Doctor, probably McGann (I think somebody else suggested this on another thread a while ago, but I can't remember who. So, just to be clear, I'm not taking credit for this idea, just repeating it and saying it would be great)