Kyoto is extremely safe. It's a smaller, calmer city than Tokyo with very low crime. The main practical issues are navigating bus routes (the city bus system is efficient once you have a day pass) and the intense crowds at top sights in peak season.
Gion district etiquette: do not photograph or approach geiko and maiko on the street — it's considered harassment and there are now official signs banning it in Hanamikoji Street. Respect 'no photography' signs inside temples. Rental bicycle is an excellent way to get around — flat terrain and dedicated lanes in many areas.