Karen Berlin Ishii, One-to-One Test Prep for the SAT and ACT - in NYC and via Skype
Most US colleges and universities do not offer single years of study except for those affiliiated with specific other institutions. You should check with the colleges to which you are considering applying to see if they offer any year abroad or exchange programs with US schools. If you are in the UK, check out the US-UK Fulbright Commission's many resources for guidance.
Most programs do not offer the option to switch to another halfway through. You might just have to end your stay and go back to your home college, but you might lose credits and not be able to enroll in courses back home for the second semester, so choose wisely!
As for what are the best schools, that really depends on what you are looking for. There are many excellent colleges in the greater NYC area. Check out The Princeton Review for their excellent online guide to colleges, as well as the College Board's online guide or the Fiske Guide to Colleges.
Some of the most famous liberal arts colleges in New York City include New York University, Columbia University, Barnard College, Fordham University, Eugene Lang College at The New School, Sarah Lawrence College and St. John's University. A web search will find you many more!