Living close to Jita can be a pain with regards to how busy the systems are and the higher population of griefers. It makes doing anything in space less relaxing, and as such I tend to spend less time undocked.
Earlier today while returning from Jita I noticed a couple of the Rogue Swarm Nests in my local system. These are the most recent date limited PVE event sites, this time based around Drones. Given it was after midnight in game and things were quiet, I decided to run them in my Legion (set up for Event Sites). I managed to do so without being interrupted.
https://community.eveonline.com/news/news-channels/eve-online-news/rogue-swarm-alert-get-involved/
The sites are slightly different in the sense the NPC’s warp in, they drop a slightly wider range of loot, and if you wait a minute after killing the Swarm Overmind, you will get another spawn. Apparently, this additional spawn can be a Battleship, but I have not seen one. Instead I’ve always got around 8 small drones, although once got around 16, and in the last site I ran there were around 24.
The site looks nice, and they are simple to run. Warp in, kill 3 mixed spawns of Frigates, Destroyer and Cruiser sized drones, then kill an Swarm Overmind. Even the NPC warp ins seem to be placed so that you don’t have to worry about getting hung up on structures.
I had noticed CCP was keen to advertise these sites could be run by anyone – and they have done this by giving the NPC rats pretty anaemic damage. I have been comfortably passive shield tanking them in an Armor tanked Zealot, with what Pyfa suggests is around 2.5K Shields and a 7 EHP/s regen.
After the first two sites, I decided I’d fit up a Zealot, and slowly head off randomly towards quieter regions running them as I go. This is the fitting I am using:
[Zealot, Event]
Damage Control II
Heat Sink II
Heat Sink II
Heat Sink II
Tracking Enhancer II
Energized Adaptive Nano Membrane II
Medium Armor Repairer II
50MN Microwarpdrive II
Sensor Booster II, Scan Resolution Script
Dread Guristas Stasis Webifier
Focused Medium Pulse Laser II, Scorch M
Focused Medium Pulse Laser II, Scorch M
Focused Medium Pulse Laser II, Scorch M
Focused Medium Pulse Laser II, Scorch M
Focused Medium Pulse Laser II, Scorch M
Medium Energy Metastasis Adjuster II
Medium Energy Metastasis Adjuster II
To make the sites as relaxed as possible, you want to be quick. Quick to warp around, quick to lock up the rats, quick to kill them, and be quick enough to rush loot drops when contested. It also helps not having to carry much ammo, be able to mindlessly tank the sites, and have enough cargo space for plenty of loot. In the dozen sites I’ve run so far, the Zealot has hit the mark well.
I am just using Scorch, which does 372 DPS out to 31+6km which covers the rat range profiles until the loot drops. I can switch in Multifrequency Crystals for 466 DPS to 11+6km, but it is not required.
Anyway – not sure how many sites I will end up running, but at only a few minutes each they should keep me amused for a little while.
Evehermit 
Been doing these sites with a myrmidon. Getting a couple of the accelerators. Biology 5 is a must to get max benefit from these.
Tractor 2
2 scripted F90
medium jump drive
2 navi comps T2
4 drone damage amp
1 Corelli Medium rep
1 damage control T2
3 aux armour pumps
5 hobs T2.
And yes, I have seen a single Battleship drone. But it just dropped a drone limb plus a random skin. I have also had a couple of time the spew of drones from the structure. But really only need to focus on the frigs/cruis – the site can be completed without killing the spew. Although my hobs pop them like milk on rice bubbles.