I am applying for a multi-entry business visa/schengen for austria and would be spending the bulk of my time in vienna. Since, I dont have any meetings over the weekends, is it possible for me to visit other EU nations as a tourist using the same Visa
Yes, you can.
Surely you have already read the Visa Information by the Austrian Ministry of Foreign Affairs.
It may be helpful to specify your mixed business/tourist intentions with the application, but if it's not like you have several weeks of either exclusively and your stay doesn't have holes (e.g. going back and forth from home), and it is not over 90 days, it should not make a difference.
As already noted in the comments, the Schengen Visa does not give you access to all EU countries (see the linked PDF), but you can also visit some countries that are not Schengen members yet like Croatia, Cyprus, Bulgaria and Romania.