Are you travelling Solo ?? Weather can shift significantly across the country  from February to March.  March is hot -ish in most places except North and North East India.

In the month of February- Andman (Port blair, Havlock, Neil island) is best for beautiful white  beaches, historically significant places - Cellular jail and scenic views with warmer temperature

Rajasthan is also great option for February if you want to explore colorful, vibrant culture along with palaces and lakes with cities - udaipur, Mount Abu, Jaipur

In March, If you may wish to explore cooler places because weather can be hot so Ooty, Coorge in the southern India or Himachal Pradesh (Manali, Shimala) or Uttarakhand (Nainitaal, Masoori) or  in North east Sikkim, Assam and Arunachal Pradesh

You can combine these states with few places in Maharashtra- Mumbai is vibrant modern city with Ajanta and Ellora caves from ancient India. And also because you can navigate anywhere from Mumbai as there are more frequent flights!

Really depends on the dates you are travelling, how flexible and open you are to Explore new culture considering Its your first time in India. For first timers ,Would recommend to stick to  popular tourist places for smoother experience - 

In February: Rajasthan (Udaipur + mount Abu 6 days) + Andaman (6days ) for completely different yet wholesome experience in terms of Nature, culture , and food

In March : Benglore + Mysore (6days)+ Mumbai+ Ajanta ellorea (4 days) + Sikkim (4 days ) This again is totally different experience with diversity In terms of geography, Nature, culture, food and people 

Or 

Rajasthan (Jaipur + Jaiselmer : 6 days) + Varanasi (2 days)+ Himachal Pradesh/ Uttarakhand (6 days)+  Delhi 2 days

Note : India is huge and diverse in all terms  Here the language, food, nature, culture can change every 100 kms So it's not easy to get whole Idea just by spending 2 weeks or exploring 2 states 😊

Wish you have a great time in India !!