A new proof of an old theorem, especially using modern machinery, could well be within the scope of the Graduate Journal of Mathematics, which seeks to publish work either by graduate students or that would be of interest to graduate students. From their website:

The Graduate Journal of Mathematics is an electronic journal that publishes original work as well as expository work of general mathematical interest which add to the literature, have pedagogical value and help make more widely accessible significant mathematical ideas, constructions or theorems...One main aim of our journal is to help researchers in mathematics in general, and graduate students in particular, gain access to important ideas and communicate interesting mathematics.

Full disclosure: I am on the editorial board. And I'd be happy to receive a submission with a new proof of an old theorem.