From what I have seen there isn’t much RP ally side in terms of public shown events as there is Horde side so your best bet is to hold your own events. I like to call out in the ‘lfrp’ channel ingame and on discord when I am going to RP in a tavern, then people will come.
You might be interested in the Cenarion Circle RP too which is crossfaction.
Stormwind is proobably the hub of RP on the Alliance side. Best place to start looking is around 19:00 server time in the Pig and Whistle tavern. As Rushorn said, asking around in the lfrp is definitely the best bet, Discord works best in communities that already know each other.