Dehli happens to be one of the most unsafe cities in India–and this is coming from an Indian-American (my old dance teacher told me about an experiment that involved his friends sitting in the back of a closed truck with a tape that played a girl screaming for help; after quite a while, only one person came to help). She definitely should not go into the slums there–or really, Dehli as a general thing is unsafe; it’s known to many Indians as well (for example, my dad, who grew up in India, made my sister promise to stay in the Dehli airport when she had a stopover there from a flight). But Agra should be fine, as it’s a popular tourist destination. Jaipur, as far as I know, is pretty safe as well. I’ve mainly stayed in west India (Gujarat and Maharastra); it’s pretty safe there as well.
Food is also important. Don’t drink the water. It’ll make you violently sick. My sister, who grew up here but is now finishing medical school in India, got very sick her first year of living in India; her body acclimatized to the water later, but it’s definitely not a good thing. Antibiotics, malaria medicine–lots of medicine.
I agree with the earlier posters–modest clothing is probably good. Nothing too showy and don’t wear shorts that are very short (bermudas or longer are probably fine). India is a pretty conservative place.
People will try to scam you in India. It’s a fact of life. She should be very, very careful about that.
Overall, though, she should be fine.