Appreciate the hushed surroundings of Piccolomini Library while perusing the books, journals and newspapers. You may be able to find some board games too.
You'll soon learn why this Siena Historical Center collection of books is a hit with travelers. If you're looking for other things to keep you busy, Siena Cathedral, Torre del Mangia, and Piazza del Campo are in this area too. They won't take very long to get to from Piccolomini Library.