The Doctor is one of the most expensive Divination Cards in Path of Exile, and a set of 8 can be exchanges for Headhunter, arguably the best belt for most builds. This means that The Doctor is also really expensive, and you can easily get a full set of items needed for some decent builds for a single card.
The drop locations for The Doctor is as following:
- Spider Forest (tier 10 map)
- Burial Chambers (tier 11 map)
It can also drop in the Shaped versions of these maps.
When farming for it, people generally tend to farm Spider Forest. It is currently one of the best places to farm experience, as well as The Doctor. The drop rate is probably the same for regular Spider Forest, but the mobs will be 5 lower levels, making them pretty bad for leveling up past 80+.
Burial Chambers tend to have a pretty messy layout compared to Spider Forest, so there's not really any benefit to running that one.
It is not really a good strategy for farming this card, except for running hundreds of Spider Forest maps and hope for the best. The card is extremely rare, and most people will farm for many hours without ever seeing one of them drop at all. Most players report that they get 1 card in roughly 150-200 maps, so be prepared to farm a lot!