There are three things that Napoleon did in his non-military time. Napoleon was of course still a sovereign of France so this would dedicate a majority of time toward this. Napoleon as a ruler was always in need of contact and information, often getting involved in the affairs of mayors and governors on minor subjects such as town finances and other minor items.

However, outside of spending his time governing France, he would be reading. Napoleon was an avid reader from the moment he learned to read. He obsessively spent his time reading during his education, reading to the point that he would find ways to eat or bathe less in order to buy more books. This would naturally continue during his years as a Revolutionary officer, requisitioning all the books on Italian history and geography for his Italian campaign in 1796 and doing the same for Egypt and any other military campaign he would lead. He did this to understand the area he was going into and the history of the people he was going to fight, for he thought it highly necessary for a commander to be well versed in history.

However, he did more reading than just history. He loved Goethe, the poet, and obsessed over The Sorrows of Young Wuther (translated into French) and even met with Goether when on campaign in 1813. Always he would have books sent to him from France and would read obsessively when in his carriage, often throwing books he didn't like out of the window as he sped down the road.

Of course, the other thing that he frequented was women. Napoleon was famously devout to Josephine until he learned of her betrayal during the Egyptian campaign, taking the daughter of a local leader (of Muslim faith) as a mistress, but sadly leaving her in Egypt to be stoned upon leaving. He would frequently have time with mistresses but many commented that he didn't spend much time, as much as eight minutes, doing the deed. However, this would end when Napoleon married Marie Louise, being faithful to her and she to him (at least until 1814). From 1810 onward (when they married), he spent more time caring and being with her and planning the education of the Napoleon II, the Eaglet.

Napoleon didn't spend his time making model ships or scrap booking, he spent his time obsessively reading.