Exploration in low sec or null sec is what you are looking for really. With exploration you actually DO SOMETHING when you log in, and really those L4s are the most boring PVE i ever saw in a game.
I don't get your "pvp is waiting and doing nothing" tbh, sure it's the case when you're camping a gate or playing dock games, but if you fly a frigate hull (frigates, inties, assault, etc) and go roam a FW zone, there's plenty of PVP to have. You or your corp didn't join FW ? Who cares really, just go flashy, it's so easy now to recover from the security status loss. I don't remember doing more than 12 jumps without having some pvp using that method. If that's too long for you, fit a BS, go on a solo roam ... I'm fairly certain PVP will happen quite fast.
In fact people shout for PVP ( or its lack of ) when the only thing they want is to win, thus they always place themselves in a position where waiting is a key factor. I recommand downloading and watching first KIL2 vids, iirc it was called genesis : sure the fittings and combat rules were a bit different, but the spirit of that vid is what PVP should be. Does he always win ? No, and far from it.
You want fun ? leave your fleet, and don't mind the isk loss.