Yes, you can apply without leaving the US. Applying through your homeland, if you apply under the skilled worker program, it is possible that at the end stage of your application, they might call you for an interview and then you would have to go there but this is not that common.
The website is
http://www.cic.gc.ca/You will have to figure out what you qualify for. If your occupation is among the most wanted for skilled worker and you have enough points, you can apply for your PR under that program without a job offer and you can settle anywhere in Canada although you must land outside Quebec since they have their own program. If you are not in one of the chosen occupations, you can still apply if you have a job offer.
If you apply under Quebec skilled worker, you should land in Quebec but after that, you may move. For this program, it helps if you know French. You do not need a job offer to apply but you can get points if you do.
To apply for PR under the provincial nominee programs, you usually need a job offer unless you qualify for something else, sponsored by family, investor etc. It is not easy to find an employer who will sponsor you so if you find one in Manitoba, you apply there, if you find one in AB, you apply there. It is unlikely that you will have many employers lined up who want to sponsor you. Most people have problems finding one.