According to edurank, the top 20 best universities for Neuroscience in the world are:
Harvard, University College London, John Hopkins, Stanford, Yale, Toronto, University of California - San Francisco, Pennsylvania, Columbia, University of California - San Diego, University of California - Los Angeles, University of Michigan - Ann Arbor, University of Washington - Seattle, University of Pittsburgh, University of Oxford, Mcgill, Washington University in St Louis, University of Cambridge, Karolinska Institute Sweden, New York University.
For the other Ivy League universities, Cornell is 21st, Brown is 85th, Princeton is 94th, Dartmouth unknown.
For the other UK universities you named, KCL is 27th, Imperial 82nd, Bristol 93rd.
Other UK universities in the top 100 are: Edinburgh is 61st, and Manchester is 70th.
Research.com puts Cardiff at 71st and Newcastle at 81st.
According to edurank, the top 20 best universities in the world for Biology are:
Harvard, John Hopkins, Stanford, University of Michigan - Ann Arbor, University of Washington - Seattle, Toronto, University of California - San Francisco, University College London, Cornell, Pennsylvania, Yale, University of California - Los Angeles, University of Oxford, University of California - Berkeley, University of Wisconsin - Madison, University of Cambridge, MIT, Columbia.
For the other Ivy League universities, ranking is unknown for Princeton, Brown, and Dartmouth.
For the other UK universities you named, Imperial is 38th, KCL 87th, and Bristol 97th.
Other UK universities in the top 100 are: Manchester is 57th, and Edinburgh is 64th.