So I've never stayed at the hotel... but I am a fan of the free stuff here to do if you go to Vegas.
1) Catch the water/fountain show.
2) Visit the garden inside the hotel.
Both are beautiful and amazing. On my most recent trip the fountain was synchronized to Christmas carols sung in Italian and the garden was all decked out for the holidays. The fountain show is every 30 minutes (I think) and the garden is always open, but generally crowded if you go in the afternoon or evening with people taking pictures.
The Bellagio also has a chocolate fountain that will temp you into buying overpriced treats and is home to O, the amazing Cirque du Soleil show.