There are a few public events that spawn near the lost sectors that you can do as well. For instance, right outside the church is that extraction event as well as a lost sector. There's also a lost sector in The Sludge near the taken public event. I forget where the last lost sector is in EDZ. You should be able to rotate the Lost Sectors with the events and farm pretty efficiently.
Remember to try to make the public events the Heroic version as long as you have some help at them. You'll get extra rewards for completing them on Heroic; usually more blues.
Some of the ones I know are:
For the extraction events with the Fallen, you need to destroy the small "container/chest" looking thing that spawns in a few seconds after the mobs and the other cover items. There is one at each site. After all three are destroyed a pile of glimmer will sit on the landscape and will need to be transmatted while you fend off a boss mob
For the injection event with the big fire shield contraption you need to destroy the vents that open and glow just before the fire shield and AOE goes off. There are three on the top, and then I think another three in the middle, then one on the bottom.
For the Cabal extraction crew you need to destroy the small fighter that comes in then kill a boss type mob.
For the Taken event with the blight you need to enter the blight bubbles, then exit giving you a buff. With that buff you do damage to the large blight orb. After a certain amount of damage it gets destroyed and a boss mob spawns that you need to kill.
For the large servitor event I believe you need to kill all the small servitors that spawn within a certain amount of time to trigger the heroic event. I'm a little iffy on this one. I've heard that you just need to destroy three of the small servitors, but I believe 4 spawn and I've seen the heroic not trigger if you don't kill them quickly.
For the walker you need to open all three bubbles with the orbs it drops after you down it. After you open all three bubbles to expose the scorch cannons another walker will spawn in and you must kill both.
Those are the ones I know of.