I have just started a PhD and I am beginning to think it is not in the area that I am most interested in! What will other institutions think if I quit and apply for another PhD in the area that I really am interested in? Should I just stick it out?

you can always change your topic, you dont have to quit and reapply.

It would probably be safest to stick it out, you may find it difficult to obtain as second position having left the first. However, I think it is unlikely you will simply be able to change topic. Funds are usually secured by a supervisor for a specific project.

Ditto Ann and Sally. You might be able to change the angle of your project. It isn't easy getting on another programme after quitting.

This is four years of your life, you want to spend four years doing research you don't like?

I know many people which changed their PhD position because they did not like the first one! You have to be convinced about why you want to change and be persuaded that the new position you apply for is exactly what you want. If you can well explain why you want to change new supervisors will probably think that you are very mature because you are not just sticking to a situation you do not like. But your chances finding a new position also depends on your CV.