Quantitatively, i would go with likert based questionnaires. Qualitatively, I would use open ended interviews. These would need to be conducted with the key senior persoaell responsible for KM at the university. Since you are looking at how to shape KM at the university, then perhaps you would want to survey those on the development/implementation side of KM as well as those senior people that use KM towards e.g strategy development…
It would help if you would build your questionnaire/interviews around a specific KM framework/s
As I get it, you do not yet have any particular or learned strategy in your university... since it requires two different approaches regarding those institutes with a strategy and those who are in pursuit of shaping one from the beginning. when you are about to shape strategies you have to study the infrastructural prerequisites. For measuring this you have to apply both checklists and questionnaires (they might have some open-ended questions but still are regarded as quantitative tools) along with interviews. Interviews are better to be semi-structured; because these type of interviews are easier to analyze. Yet don't forget that in higher levels of managerial ranks although these type of interviews are valuable, but maybe based on the nature of the organizational culture a Delphi method or sometimes brain storming session would also be invaluable.