Some hospitals have nurse externship programs you can apply to & those are actually paid positions. The good about this is that sometimes, hospitals will offer you a job once you graduate & get your RN license.
I work for the VA & I know that the VA has a program called VALOR (Veterans Affairs Learning Opportunities Residency) & every year, we usually get about 3 senior students. I don't know the details but I know that it's a pid position. Also, I've worked with a few nurses who were in the program & stayed after graduation.