Tip: You can do Scenarios while in queue for Looking For Raid/Dungeon.

It's not well publicized, and the UI doesn't really explain this, but the scenario queue and LFR/LFD queues are concurrent.  If you queue for both as dps, your scenario will pop up almost immediately  When you’re done, you’ll be 15 min further into the LFD/LFR queue. Sometimes that’s enough to put you at the head of the line, putting you in LFD/LFR immediately.

Basically, you can spend the time waiting in queue for LFR/LFD by doing scenarios instead of dailies (or trolling trade chat, etc.) if you prefer.