Assistant Professor at my state university, Research Scientist at my Ivy League, or both?
There is nothing against having a joint appointment. I would take both! At 20%, you gain from networking at the Ivy, and show up once a week...or even half day to attend faculty meetings or seminars. However, focus your research at the State school. In return for 20% support, you must co-list the Ivy in pubs and seminars you give. I’ve done this before, and it’s not hard. Good luck!