What would be the best place to move in London, and the best way to move there?

The UK is not short of nurses, in fact many nurses are unemployed. The only non EU nurses who can get a visa are those who are qualified and experienced as theatre or neonatal nurses. You also need to be aware that the UK health system and nursing education is completely different to the systems in the USA, and to work as a nurse in the UK you must be registered with the NMC. http://www.nmc-uk.org/Registration/Joining-the-register/Trained-outside-the-EU--EEA/ You really need to do your homework.

Basically you won't be able to. Nursing is not a 'rare skill' enabling non EU citizens to obtain a work permit.Forget the idea.

I can see from the spelling "Pediatric" that your American. Thankfully its VERY difficult for people of your kind to move here. I doubt you will anyway. Keep dreamin Yank but we just dont like ya.

Just do some research, there are plenty of websites which carry detailed descriptions of various london neighbourhoods. Check out sites like Gumtree if you're looking for a flatshare, living with others keeps costs down. Then again that's true anywhere. Moving to and working in the UK is not that easy, visas are hard to obtain unless you have special skills and recently new restrictions were put in place. From the looks of it nursing is not exactly in demand. You could try for a youth mobility visa (good for a year or two) but I think it is restricted to certain countries, I know a few people who have gone that route but they have all been Canadians or Aussies. Dual citizenship is a possibility but I'm not sure what the conditions are and it is not as easy as some people assume. You will need close family ties to the UK. Dual citizneship with another EU member state might also gain you entry but don't quote me on it. Once again though, you will need close family ties to the country. Some are more liberal then others at granting citizenship but it seems wrong to go through the process just to get a passport for a year especially if you have no ties to the place anyways? Be careful. Best of luck.