You should be fine in most places as far as safety goes. When in Punjab you can always visit Harmandir Sahib AKA golden temple. You will need to check your shoes in and have your head covered at at all times. The temple has a place to check shoes in and scar pickup to cover your head. no photography inside the main temple and no tobacco/alcohol items allowed inside. Do try the meals served there. The meals are called "Langars". You should also attend the Wagah border ceremony. A change of guard ceremony that happens near the indo-pak border. Near the Chandigarh you can visit Sukhna lake and the Dorahara Fort.
As for Delhi red fort would be a good place to start. India gate and Amar Jawan Jyoti have historical/military significance. The national museum at New Delhi houses several fascinating historical artifacts
While in Delhi beware of "beggars"! do not give any money to them! their sole purpose is to empty your wallet. Always schedule your travels and use a cab company like uber. The tuck tuck/Auto rickshaw drivers might try to fleece you considering you are a foreigner. Don't kiss women(or men) for you might get thrashed by their brother or something.
Always plan ahead. India is a chaotic country! As long you know you what you are doing and have planned ahead you will fine