I honestly think public libraries should be allowed to use some of their money to advertise and create a brand for themselves. For a lot of people the thing deterring the usage of library is simply the idea that it's unexciting or doesn't offer enough, while usually a coffee shop is pretty much equal or worse. Of course it'll lead to people complaining how their tax money is being used for ads, but it makes libraries reach a larger audience and, in economic terms, improves well-being of more people.
Are there such arbitrary restrictions on budget spending by public libraries (in which states, or is that a federal thing)? I can accept that public libraries might be somewhat underfunded, and choose to not advertise -- but it sounds strange that they are somehow forbidden to do so? (At least here in Norway most of the public libraries does quite a lot of advertising -- it's hard to imagine any service remaining visible if it's banned from marketing...).
I believe (from second-hand sources) that many libraries in the US are required by their funders (state and municipal governments) to spend a certain fraction of their budgets on buying books.
Well, that doesn't sound too crazy ("you need to spend some part of your budget on actually being a library") -- but that shouldn't exclude all marketing -- unless that fraction is very high indeed...?