It has been observed through history humans have been willing to spend up to half an hour each way on their daily commute. It doesn't matter if they are walking, biking, driving, flying, or something else, half an hour is the typical budget. Some people do go much longer (transit often allows for little longer if it is otherwise good enough that you can do something else while riding) , but that half an hour rule tends to stand across all cultures. Anyone who has farther to go will move.

That is daily commutes though. People often lived in a village near their field, but every few weeks would make the much longer trip to the town (city?) where there is a bigger market day. You don't do this every day, but for a once or twice a a month trip it can be worth it.

So back to your question is this a regular daily trip to the library - half an hour is the most you get, so you need to have multiple locations in all but the smallest towns. If this is however the big central library with a special collection of some sort people will make a 2 hour walk every few weeks if there is something special you cannot do at the local library.

Realistically I'd aim for a small library within 15 minutes for everyone because shorter distances makes it more likely people will go. You should try to have basic market places in the same location: basic groceries, a couple cafes, a few other shops, doctor and dentist offices.... That is the basics everyone wants close to home in one "central location" so it becomes habit to walk there a few times a week after work. People might go elsewhere to "costco" for their main shopping, but when you just need a cup of sugar this is close enough to send a kid alone while you finishing supper.