Media planners are employed by a variety of different sorts of companies / organizations.
Firstly, the advertising agency. Media planners are often employed by traditional creative, as well as direct marketing, advertising agencies. In this scenario the media planner is able to work closely with those creating the campaign (the account planner, the copywriter, the art director, and so on). This obviously has its advantages (integration of work).
Secondly, large media companies. Such companies might focus on media planning, as well as on media buying, sales, marketing, and so on.
Thirdly, niche media planning companies. These might focus on digital planning or traditional planning.
For graduates looking for media planner jobs, the important thing to find out is the type of media planning company / organization you would like to approach first. Or if you have applied for some vacancies, to do some research on those media planning companies that invite you in for interview. It's a good ideas to understand all the different sorts of companies / organizations that employ media planners, anyway, but focusing on what a particular media company does is really important.