For the animal/biological side of things, I can highly reccomend the Zoology museum at Aberdeen University & the associated Natural History Centre/Cruickshank Botanic Garden. IIRC, the museum-rep body rate it second in the UK whilst the more general/anthropolgical Marischal Museum is well worth a look too.
http://www.abdn.ac.uk/zoologymuseum/
http://www.abdn.ac.uk/diss/historic/museum/index.shtml
http://www.abdn.ac.uk/diss/historic/museums/
Also, if you like things aeronautic, the NMS Museum of Flight at East Fortune is a gem, as indeed are most of the other NMS collections.
http://www.nms.ac.uk/flight/home/index.asp
http://www.nms.ac.uk/nms/home/