Queens Club is invite only, you need to know someone who's in there and then the club needs to accept your application. I think it's quite a bit more expensive than your typical club but that's to be expected.
Thinking of Queen's reminded me of the tournament and I just got myself a ticket to the 3rd round day on Centre Court!
The whole Queen's complex has a security gate so doesn't surprise me to hear that it's invite only - shame.
Wimbledon Park looked a lot more accessible, though the hard courts were separated from the grass courts by a big hedge and so I guess the grass is a private club. In fact, from the look of them, they might be the practice courts during the Big W