People often get fixated on doing internships at the most well-known organisations in the sector they want to work in, but the truth is that experience anywhere can be incredibly valuable an in fact is often of a higher quality at smaller companies.
Take journalism for example: a week making coffee at Vogue magazine may look great at first, but compared with a month at the local paper is actually not too useful. At a local rag you are likely to take on real stories by yourself, conduct interviews, write longer pieces (at Vogue you might not write anything at all) and generally do more real work. This will boost your portfolio and look more impressive to perspective employees or university course leaders in the future: they'll know what a quality internship looks like and will give you credit for it.
The key is to find somewhere you’ll really be able to learn the skills you’ll need for the career you want, rather than trying to go in at the top to the place you actually want to work. If you want to go into psychology for example, it’s unlikely you’ll be able to shadow a therapist, but how about helping out at a local hospital: it will give you experience dealing with people and being in a clinical environment, and is a realistic aim.
Image courtesy of Sandro Katalina