AN SBL SESSION ON The Future of Biblical Studies: What Research Still Needs to Be Done? has been organized by Patrick George McCullough for the November meetings in San Francisco.
Good question! Reception history is very big right now. And there is a surprising amount of basic textual criticism that still needs to be done, although this involves very technical work. Some of it involves working with Armenian or Ethiopic or the like, but there's quite a lot of work still to do on the Greek Septuagint. And as for cognate fields dear to my heart, the Dead Sea Scrolls are fully published, but critical analysis of them still has a long way to go, and many Old Testament Pseudepigrapha and New Testament Apocrypha still cry out for good critical editions, let alone further study.
I'm sure there's much more, but that's what occurs to me off the top of my head.