As you walk around the city you'll find that not all the buildings are ancient, some are avant garde examples of modern art. We wanted to stay at a Ryokan in a Japanese-style room. But, in Kyoto, that location was fine and very safe. We had a very large Japanese-style room with tatami mats and futons for sleeping. Not only are the temples and castles 400 - 600 years old, but so are some of the restaurants.
Lunches are almost always a great deal, while dinners are often more expensive.
Ramen and udon places are generally less expensive dinner choices while sushi and tempura are great deals at lunch time. An interesting option for dinner is to try a restaurant in a department store. They're unlike department store restaurants in America as their quality is more like that of a local restaurant. At one of the department stores near our hotel they had eight restaurants, each with a different specialty such as Chinese, sushi, ramen, tempura, etc. They even had a French bakery, a Harrod's outlet, and made their own ice cream and gelatto.