Which university has the best nursing and marine biology programs?

A good place to look up U.S. school rankings is the U.S. News websites. You also need to determine how you define "best."
There are rankings by class size, by location, by competitiveness, etc..

The rankings do change from year to year.

And of course there are the Ivy League Colleges.

Marine biology and nursing are two very distinct professions. The good news is that both require lots of biology, chemistry and an understanding of how the world works. Having taught in both environments, I assure you that courage, persistence and situational awareness are important personal traits that will determine your success in either fields. Nursing in college is a little more hands-on unless you go to a place like UC Santa Barbara, or UC Santa Cruz, or Scripps Institute of Oceanography, etc. You simply cannot afford to be the least bit squeamish about animal tissue in either case.

Most universities that have a good medical school also have a good, high quality nursing program. I suggest you plan on getting at least a MA in nursing if you go that way. The marine biology career will almost certainly require a Ph.D. The University of Cincinnati and The Ohio State University have excellent schools in both areas. In the SW, Baylor in Waco, TX is excellent.