I would check with the neurosurgery department and see what kind of research they are doing. You can start with something like a case report (which isn't really research but it will get your foot wet) and then perhaps get more involved. Chart reviews are another type of research that can be from simple to complex and answer some good clinical questions in regards to neurosurgery. There is also research in techniques and devices. Basic science research in cerebrovascular disease or oncology is fairly common so there may be a labs at the medical school doing this type of work. To see what neurosurgery research is published check out the Journal of Neurosurgery or the journal simply called Neurosurgery.
