Well, given that the PvP season ends this coming Tuesday, the common wisdom has been that we're going to see 7.0 drop next week as well. Seemingly confirming this, a new patch has arrived on the PTR labeled as "Release," meaning it's a build they feel confident enough to release live - it doesn't mean they won't make changes, but it means that they're basically good to go.
So what should you do in the meantime?
Patches, especially big ones, tend to break addons. So update the ones you can. Some addon-makers might not be totally keeping up with things, in which case some of your addons might not work for a couple weeks. But update the ones you can.
Sell Garrison Follower Armor Items:
Let's face it, you're not going to be managing your Garrison Followers all that much after we've left Draenor behind. You probably don't need to keep all those armor and weapon upgrades.
Well sell them off now! You can get a pretty large amount of gold for them at a vendor now, but in 7.0, they'll be worth only a few copper a piece. Sell now!
Dump Other Stuff You're Not Going to Use:
Got a bag full of ship equipment? Get rid of that crap. You're not going to be using it. Got reputation items for Draenor factions? Just use them now.
Oh, But Hold On To Your Gear:
Hold on to every little bit of soulbound gear that your character would realistically use (if it's cloth and you're a warrior, feel free to vendor/de that stuff.
The new transmog system will save the appearances of all the gear in your inventory, bank, and void storage, after which you'll be able to toss it all out (though I know I'm going to be holding on to some pieces for pure nostalgia.) But it won't save that gear until the patch actually hits, so hold the hell onto it for just a few more days!
Use Up Baleful Gear:
Nothing's really happening to the Baleful stuff as far as I know, but the Demonic Invasions are going to be rewarding better stuff. However, the demons in said invasions (particularly the "no really, this is a raid boss" demonic generals) hit hard enough that they seem to expect you to be wearing something a little better than your Nagrand leveling greens (that said, you'll get credit even if you just sit in the zone, so don't worry if you find yourself spending several minutes as a ghost over the course of the invasions - you still get your loot boxes and Nethershards.)
Good Luck on that Legendary Ring...
You will no longer be able to start the Legendary Ring quest chain, but if you're on the second stage (the Highmaul one, I think,) you will be able to continue for the next couple weeks, until the expansion itself lands.
Starting it now will not give you enough time to complete the whole thing, I'd guess, but if you're on the last stage, I'd start making sure I was running all of HFC every week to maximize my chances of getting the thing done.
Run as Many Gold-Gathering Follower Missions as You Can:
Garrison gold is getting nerfed hard so that people won't feel compelled to return to their garrisons. So get that last burst of gold while you can!
Bid a Tearful Farewell to Abilities You'll Miss:
Every spec is getting pared down, and while I think that in almost every case it's a good move for the game's design, I'll certainly miss some of them. So farewell, Holy Wrath. Goodbye, Dizzying Haze. So long Plague Strike (actually, I never really liked that guy.) See you in another life, Magma Totem. Via con Dios, Dispatch. Safe travels, Hurricane. Keep fighting the good fight, Exorcism and Hammer of Wrath. And a special moment of silence now for Gladiator's Resolve. Maybe some day we'll have a dedicated sword-and-board melee spec, but you were never long for this world.
But the overall design of the 6.0 Arms Warrior? You go back to hell where you came from!
I still have not gotten a Grove Warden mount. I hate pugging raids, which I often experience as "all the toxicity of LFR, but you never down any bosses!" The good news is that even if you don't get it this week, you'll be able to keep getting it through August until Legion itself drops. There is another magic-looking moose mount for Glory of the Legion Raider, but it's A: Nightmare corrupted (read: black, white, and red, like a White Stripes album) and B: doesn't have the cool glowing eyes or antler runes or fancy barding.
But fret not if this week doesn't work for you - you still have over a month to get this guy.