One of the ways that insurance companies try to control costs is by contracting with certain doctors. If there's a specific doctor you want to see, then you'll want to check if a given plan will allow you to see him or her without any additional costs.
Plans are often distinguished by your ability to see different doctors. For example, with a health maintenance organization, or HMO, you're required to choose a primary care physician from a list of given doctors. If you want to see a specialist, you'll need that primary care doctor's authorization to do so. With a preferred provider organization (PPO), you can elect to see specialists without your regular physician's approval, but unless you want to pay additional fees, you'll want to select a specialist that's within that PPO's network of contacts.
Insurance plans may also only cover care that's provided at certain hospitals, so if there's one in your neighborhood, you'll want to check that you can go there instead of the one across town.