You should contact your university to find out whether they have a way for university members to access library subscriptions off-campus. For example, the university I'm at has a VPN (virtual private network) system - something like a proxy, I guess - which allows you to access JSTOR, etc. I think other US universities have similar systems set up.
You will not be able to access all articles from JSTOR, in any case, only those journals for which your university has a subscription.
IPHIGENIE: Kann uns zum Vaterland die Fremde werden?
ARKAS: Und dir ist fremd das Vaterland geworden.
IPHIGENIE: Das ist's, warum mein blutend Herz nicht heilt.
(Goethe, Iphigenie auf Tauris)