There are a handful of guilds on WrA – especially Hordeside – that push heroic and mythic. is the only one that’s coming to mind at the moment, but I know there are more whose names I’m blanking out on. Some have recruitment threads on the forum here, so I recommend scrolling through, and also checking out this thread in particular:
There are also many RP-centric guilds; but while some guilds focus on both RP and raiding content, most emphasize one or the other.
Most storyline-driven RP, with long-term character relationships and campaign arcs, is going to be guild-based. However, there are walk-up RP and public events to be found outside of guilds, usually with a casual/social focus. A lot of public events get advertised here on the forums, so check the first page for those as well!
As far as random walk-up RP goes, you’re most likely to find it (if playing Horde) in a few districts of Silvermoon (especially the Royal Exchange), and in Orgrimmar’s Valley of Honor. Those spots are rarely completely empty, but they seem to be most bustling around 6-9ish PM server time.
Be aware that you’ll almost never find walk-up RP in Warmode, so if you tend to have that turned on, turn it off when looking for people to RP with.
Also, I sincerely recommend rolling a low-level alt to check out the server environment for yourself, in a few different places at your usual playtimes, before you make the decision to pay for a transfer.
Is there any specific race you’re planning to mostly play, or a theme of RP you’re interested in? Like adventure, criminal, political, slice of life, etc?
Edit: Links are hard, guys.