Pretty hard question to answer... the most coveted research would
presumabley be the research that is consistantly found in the highest
impact journals. Nature neuroscience has a lot of electrophysiology so
long as it has a molecular spin...
If you're interested in what "neuroscience" involves then grab a copy
of Nature Neuroscience or the Journal of Neuroscience (and maybe even
the Journal of Neurophysiology) or Neuron and have a read. It's a very
diverse field, from computational neuroscience to cognitive psychology
to molecular biology.
It's not so much about the place (though that certainly helps when it
comes to getting publishing in big journals) it's about the lab. Find a
topic that interests you, and then find the biggest player in that
area, and then see if he's got a PhD for you.