Thought I'd wade in here, as this is a topic that is often discussed in my circles.
The Mighty Karori Cougars have only played at KP once this season (first game as well, seems like forever ago!), but we've been at Ben Burn and Wilton a few times and generally try and get back to KP for a bevvie afterwards. However as our league is a bit of a travelling road show, we very rarely will go back to KP after away games, especially since team members are spread out all over town. Of course Karori being where it is doesn't help either.
On a bit of an aside - the facilities at Wilton and Ben Burn are a joke - only one changing room and 3 showers (I think) at each. We played Wairarapa at BB not long ago on a particularly cold Saturday arvo and there was no hot water at all, no a great way to start a long car journey. Similarily we played Waikanae at Wilton and after the game there were four teams trying to get changed in the one, very cramped, changing room. Not a good look really for these teams that have had to travel a long way.
I don't think we have ever been "invited" back to a teams club rooms while playing away, however after playing at Kapiti on the weekend (surely one of the best pitches in the region?!) the majority of the team stayed for a beer and a feed. We usually stick around for a beer after most games though.
As stated by someone above, I imagine these are problems facing most Karori teams.