一方 literally means "in one direction." This phrase is often used as a way to contrast two different statements. It can also be translated as "on one hand" or "in contrast"
のに means "even though" and is also used for contrasting statements
一方なのに would therefore mean something like "even though it's this way"
So, in the context of this sentence, it says:
"Even though the Japan of today has been dragging itself through a long recession, I don't really see any sort of leadership from the government."