There are so many spots in Kyoto, depends on what you mean with near by. But Nijo Castle, Heian Shrine, Maruyama Park, are not far and some of my favourites. A bit further a field Philosopher's Path, Nasenji Temple and the Lake Biwa Canal, Ginkakuji (not to be confused with Kinkakuji) are other favourites. But as timing can vary a bit across the city, talk to the hotel about where is best when you are there.