The accreditation process is long, expensive, and complicated -- there are plenty of perfectly fine nursing programs "out there" that have chosen not to pursue accreditation, and there are some poor-quality accredited programs (just as there are plenty of non-Magnet hospitals that are good hospitals and good employers, and some Magnet hospitals that are crummy on both counts).
However, having said that, you are much better off in terms of your own professional future if you attend an accredited (NLNAC or CCNE, the nursing-specific accreditations) program. Most programs of higher education in nursing, including most graduate programs, require that applicants be graduates of an accredited program in order to be eligible. And it's not just a matter of school -- a growing number of healthcare employers will only hire graduates of accredited programs, including some of the most desirable healthcare employers in the US (the entire US military, the entire VA system, most big academic medical centers, lots of other hospitals ...). IMO, there's no point in closing off so many future educational and career opportunities to yourself this early in the process.
Best wishes for your journey!