Keep your eyes out for Flag/MRP users, try walking around and wear RP clothes when in town, talk to friends and even NPCs in /say and /me and be IC! Try staying on the ground instead of flying; the main Horde RP hub has no flight, and people find each other for random RP there all the time!
Here's some ideas; if people have preferences or more info, let's hear them!
Cathedral District: This is the go-to for other Servers. The fountain in the center, the gazebo in the back, the lake shore, the nice cemetery. My guild meets in the old Argent Dawn building on Wednesday evenings (unless we're on one of our old school raid nights).
Olivia's Pond: There was a "Pond Group" in Cata, mostly alts of Horde-main players, or people who've since left our server/game so far as I know. Or they aren't as seen since we all moved to Pandaland. The farm, the lakefront, it's all very nice for hanging around and RPing and/or fishing.
Mage District: There are 2 weekly events here; Inkwell on Tuesday evenings, in the little library across from the Stockades, near Robby Flay's stand. The other is Wendy's Open Air Bar on Fridays by the well in front of the Slaughtered Lamb; it's a nice little park-like area. Speaking of, there are 2 bars in the Mage District; The Blue Recluse and Slaughtered Lamb. Anyone using them semi-regularly for RP?
Dwarven District: The Golden Keg is a good bar, there's always Cutthroat Alley for hanging out (with its own little shop entrance, The Shady Lady). Also leads to the lake and Olivia's Pond.
Old Town: The Pig and Whistle and the Command Center are both good RP spots. There are some little nooks here for fishing quests too, and the center alley with the poison shop, that used to be a quest spot.
The Keep: Dragoons don't use the space regularly anymore, but it's always been great for RP with the Petitioner's Chamber, the Garden, and the Library. Even the War Room could be a good spot given the current clime.
The Harbor: Stationary boats, lots of dock space, nice balconies.
I focus on Stormwind as it's "central" to the Alliance and has portals to pretty much everywhere, even back to Pandaria. But with Portals from the Shrine to other cities, it's handy at this time to get to those places.
Darnassus: It's got lots of open buildings and lovely scenery, and is perfect for Night Elf, Draenei, and Worgen RP especially.
Ironforge: There's a weekly lore lecture on Thursday evenings in the Hall of Explorers, with drinking in the Commons Inn, and I know some characters make their IC homes there. Who else is RPing there?
The Exodar: Not a lot of random buildings here, sadly, but the beach is nice, and the outer area can be nice. The portals to and from Darnassus help too.
The Shrine: Our Shrine in Pandaria has plenty of space! There are a couple balconies and rooms that can just be hung out in (particularly the one with the musicians on it) as well as the terrace. There's a nearby pond, some shade trees out front. There are a lot of empty places in Pandaria that can make for good RP spots. I keep thinking the hilltop from the cinematic is a great picnic/party/wedding spot.
Where do people want to look to find other RPers for open, random, walk-up RP? It's a RP server, we should be able and willing to RP in public!