Hope you have come to India earlier too,,otherwise comming to India and not visiting Taj Mahal, so if this is the first time you should visit Taj Mahal. Can do same day tour to Agar from Delhi or can stay overnight in Agra to as there you will find hotels of all budgets.
Going to Goa at this time of year will be a bit hot for you as you are comming for a very cold place, but its ok to stay in there for couple of days to have a feel of the city.
Also should visit the capital city of Rajasthan - Jaipur to see the City Palace Museum and Janter Manter (a unique observatory in the world), Hawa Mahal and Amer Fort. Can also visit Choki Dhani in the evening for traditional rajasthan meal served in Rajasthan style and an Rajasthani village kind of set up.
Suggest the following route:
15 april - Arrival in Delhi
16 april - Delhi - visit the old Delhi and New Delhi parts- must visit Raj Ghat, Jamma Masjid, Chandani Chok Mkt., take a Rickshaw ride around Red Fort Area and passing though the busy and narrow street of old Delhi an experience.India Gate, Sansad Bhavan, Rastrapati Bhawan and other government buildings. Can also see a sound of light show at the Old Fort or Red Fort in the evening at 1900 hrs onward.
17 april - Delhi
visit the New Delhi part visit the Qutab Minar, Lotus Temple (bhai temple), Humayun's tomb, Akshardam Temple and in the evening visit the Sikh Temple - Gurudwara Bangala Sahib, Sacred Heart Cathedral and Birla Mandir (Laxmi Narayan temple) to attend the evening Hindu prayer - all in close vacinity.
18 april - Chandigarh, visiting some of the parks in town
19 april - Chandigarh to Kalka and then take a toy train to Shimla
20 april - Shimla - visit the Jhaku Temple and old Imperial Buildings and spend the evening time at the Mall where all the town & tourists gather.
21 april - Shimla - Delhi
22 april - Delhi - Agra
23 april - Agra - Jaipur
24 april - Jaipur - Delhi - Mumbai
25 april - Mumbai - must see Prince of Whales Museum, Elephenta caves, Chopati, Marine drive and if interested can also see some Bollywood film shooting at some film studio.
26 april - Mumbai - Goa - flight
27 april - Goa - visit North Goa
28 april - Goa - Visit South Goa
29 april - Goa
30 april - Goa -Delhi flight
In case of any doubts..write again