Going through stuff; where can I hang out in the city centre for free?

As title says, looking for ideas for stuff to do so I don't trap myself alone in my home all day everyday. Need to get out and about a bit and find somewhere I can relax at. I'd hang out at coffee shops but it would require me spending and drinking etc. I was thinking the library, but what other places can people suggest? Obviously there's outdoor spaces like peace gardens, winter gardens and the new park, and meadowhall (too busy for me though), but maybe there's some nice places I don't know abotu where i could just spend hours reading a book etc.

Thanks all :)