Large or small setting where should I focus my first job search.

Honestly, the job market it so competitive right now, especially for new graduates, that you should apply to both locations and start your career wherever you get a job offer.

But if you're given the choice I would suggest the larger hospital. Larger hospitals tend to see a wider variety of sicker patients, have more job openings, and offer more opportunity to transfer to another floor within the hospital. Sometimes experience from a larger hospital is valued more than a smaller hospital. All in all, the larger hospital gives you more options for the future.

Yes. Apply everywhere I don't know where you live but bottom line is large metropolitan centers are not hiring new grads and the ratios of who's looking for vacancies is about 2000:1 in southern California. If you are serious about getting a job you might have to get out of your comfort zone and look in rural areas, but you might get lucky and get a job right away as some people do. If it looks like is getting hard don't think to much and go to rural areas where they still hiring because new grads might just discover that too and even these places might be filled up!

Large and small and anything in between. And the bordering states as well. :)