So many libraries have lost the basics that so many people want:
Somewhere quiet and cosy to sit and read, with newspapers and magazines.
Separate from that a nice space with desks and natural light to work, with keepcups or similar allowed.
(Single-sex) toilets, this might actually be the most important factor.
Sensible, predictable, opening hours.
Some optional extras that would be nice but should come so far down a list below the above:
Tea or coffee facilities for a donation would make a library competitive with cafes for students and wfhers, and would be nice for elderly people and parents too. You can have restrictions on what cups people are allowed and where (the Bodleian allows cups so I reckon other libraries can).
Quiet companionable clubs - a crossword club, knitting, jigsaws.
Children’s activities - lowkey and frequent better than too busy and chaotic once a week. Something aimed at mums with babes in arms in addition to the usual rhyme time type things.
But mostly some quiet spaces and a usable toilet please.
Editing to add - someone else mentioned creepy men at computers. This is such a problem and a friend who works with the police said it is a known thing that perverts use library computers to look up god knows what because the history is then wiped. Have the computers facing out into the room where a librarian can see the screens.