Academic vs. non-academic. There is a continuum of jobs ranging from large academic research institutions to small private practices. The largest of academic institutions will emphasize subspecialized care, and each faculty member will likely have an emphasis on research, teaching, or service (and sometimes all of the above). Teaching and working with trainees is a large part of these positions. Case volume and call are often less, but salaries are also often less and physicians are most often employees of the hospital system. Mixed type institutions would include smaller academic centers, non-profit/private health systems, and other hospitals which may have trainees and be very subspecialized (e.g. VA hospitals, Kaiser, etc). These institutions often combine features of big academic centers and private groups.
Private practice groups are at the other end of the spectrum and range in size from less than 10 to more than 100 physicians. Case loads and call may be higher, but there also are also often fewer administrative and teaching requirements. Specialization varies widely, with smaller groups tending toward the general and larger groups as subspecialized as academic centers. Radiologists may be part of a physician group which owns the practice and sometimes imaging centers or equipment. In this case, physicians will often be on a partnership tract in which they are group employees for several years before becoming partners and sharing in the profits of the group. Depending on group structure, salaries may increase significantly upon becoming a partner. If a group owns imaging centers and equipment, there may be a monetary buy-in to become a partner. Other groups are salaried employees of the hospital system or physician group.
Subspecialty content. It is important to think about how much you wish to practice in your desired subspecialty, in this case neuroradiology. With neuroradiology being a significant component of radiology overall, it will likely be a big part of any career. Some people may like the challenge of covering all areas of radiology, while others will prefer to do predominantly neuroradiology. This will somewhat guide you in terms of group size. As part of this, you may think about areas in which you would prefer not to practice (e.g. non-neuro procedures, mammography), which may be a consideration. In general, there has been a tendency of private groups to consolidate and become increasingly subspecialized. In many groups, call is general, but larger groups may even have specialized call pools for neuroradiology.
Geography. Where you want to live is a huge consideration. Many of you may want to stay in the area where you have done your training. Others may seek to return closer to family. Still others may not have a geographic preference at all. It is important to think about what you want, as some geographic goals can help guide your search.
Overall, it is valuable to place some combination of constraints on your search. You may prefer any job type in a specific area if you are very eager to move closer to family. Alternatively, you may be looking for the best academic job in a city, regardless of region.