3 World Heritage Sites of Agra must be visited Taj Mahal Agra Fort Fatehpur Sikri in Delhi also 3 UNESCO World Heritage sites Red Fort Hamayun Tomb Qutub Minar are worth visit along with it there are no of other places to be covered but don't miss these Heritage sites
If you are starting from Bangalore then you need to know perhaps places in Delhi and Agra. So in Delhi so visit:
1. Red Fort
2. Qutab Minar
3. Lotus Temple
4. India Gate There are many other palaces but you don't seem to have lots of time. Agra
1. Taj Mahal but of course
2. Agra Fort
3. Fatehpur Sikri