Unfortunately no specific places like this exist to my knowledge, but I have always found the fountain in Atlas Park to be teeming with life and when not battling evil I go there to roleplay and socialize. It serves the purpose almost as well, though it would be a nice feature to be able to change into "civvies" and go out on the town.
Wouldn't it be interesting if you could only meet and interact with certain contacts if you owned an "alter ego" and thus had to become him/her? Of course, for a hero WITHOUT an alter ego they could access the contacts no problem, but the ones who choose this feature would need to find an available "phone booth"
Heh heh heh...
Yes, that's exactly what I was getting at. What kind of superhero doesn't have an alter-ego? It seems such a deep-rooted part of comic book superhero mythos that I'm surprised it wasn't included in one way or another.
I believe they explained that there was no need in this game, since the city has so many heroes nobody really cares who you are. <shrugs> A secret identity would STILL be cool. 
Honestly, I hope that in future upgrades we get a feature similar to this... however, if it's beyond the devs to include, we would DEFINITELY be able to role play the feature, and here's my thinking:
Ok, we know that down the road we'll be able to hopefully "Upgrade" our costumes, right? Well, what to stop us from changing the costumes to inclued civi clothes, and being able to change back later? At least this way, we could roleplay out alter-egos... anyone else interested in pursuing this avenue?
<(
My secret identity is Silva Lemae.
Now it is up to us as the role-players to give that name a purpose.
)>
I'm new to Paragon city and have yet to find a hangout for off-duty heroes such as myself.
Haven't come across a bar or club or any type of off-duty hang out as of yet and am wondering if any other heroes have found such shelters to hang loose at.