I work for a library service and, like Bathsheba, we constantly ask ourselves the same sections. We're winning, though, and numbers are increasing.
All sixteen of our libraries do the things you said, Ethel, although the libraries that offer tea and biscuits tend only to do so to the pensioners that get brought in on our minibus. We do a housebound service, too, and run two book buses for the kids as well as loads of other schemes for older kids - family workshops, study support and a forthcoming children's literature festival. In fact, our Children's Service manager (my boss, actually) has just been nominated a national reading hero and is off to number 10 very soon.
Our latest thing is sofas and magazines, where people can just come in and sit and read (or not, as they wish) a magazine or two.
If anyone hasn't discovered their library yet, give it a go. Public libraries have changed a lot in recent years and you'd be surprised how much they have to offer. Where else could you access the internet for free, and borrow top ten DVDs for a couple of quid a week? In the current, cash-strapped climate, it's got to be worth a look.