I would suggest two things:

1. Casual places to hang out at and do nothing but socially interact - but importantly, where one is encouraged to hang out both by the environment and through offering low-key entertainment and consumables. Basically, space pubs. I should be able to sit down and have a virtual beer while chatting with a friend about some indy jobs I'm doing. And now a newbie wanders in, looking lost. Well, I might just shout him a beer and ask if he want to sit at our table. That sort of thing...

2. Meaningful collaborative tasks that pay out reasonably, for which one can casually sign up with other people, and where the game provides dedicated meeting places, easy sign-up mechanisms and a modicum of built-in protection against victimisation through other group members (not outsiders). Basically, space adventure guilds. The best way of finding out that one can have fun playing with someone is to play with them, yet currently this is largely restricted to corps. One can shout for assistance in local, but there is little in-game encouragement for this. It should be possible to log into EVE, think "I fancy doing this mission, let's see if I can find some people", warp to a specific place where people congregate, arrange for a group and then head out to do it without having to worry overly about backstabbing (other players attacking the group is a different matter).