Oh you can totally RP without a hideout, it's just a bit awkward to find some locations for it that aren't spammed with other people's emotes and such or have a much of PCs running by constantly...

Some good places though are inside the buildings in Summerford Farms, the Bar at Vesper Bay is a nice spot too. There's a farmhouse out by the lighthouse near Moraby Drydocks I discovered recently seems to be a nice spot to RP in.

In the main cities some decent spots are Apkallu Falls in Gridania, The Bismarck in Limsa Lominsa and the central square area underneath the Husting Strip in UlDah.

Also there's a restaurant above Rowena's House of Splendour in Revenant's Toll now that is just ideal for a bit of RP.