Flights to Goa
There are two good reasons for flying to Goa. You may think the first reason is obvious; the beaches. However, even though Goa has much better beaches than Brighton and Blackpool, the beaches are not as good as those in south-east Asia. The reasons for choosing to fly to Goa are:
It is possible to get very cheap charter flight deals to Goa, as little as £90 for one way flights from London Gatwick to Dabolim airport in Goa. The best deals are usually in late January and February but good deals can be also be found from October to early December. Often the deals are offered at the last-minute, just a few days before departure, so you need to be flexible. Also remember that most nationalities need to obtain a visa before travel to India. From London, the flight time to Goa is about 12 hours, usually there is a refuelling stop in the gulf.
From Goa there is a direct train to the ruins of Vijayanger at Hampi. Or you can take an overnight train north to Bombay or south to Kerala or Bangalore. You can also fly from Goa to Bombay, there are many flights daily and the flight time is only half an hour. You could take long distance buses but I don't recommend this option.
India is different and will be a huge culture shock to the first time visitor. Many travellers swear never to return, which is a shame as they are missing out on many amazing experiences. To minimise the culture shock it is best to choose Goa as your first destination in India. Goa has many of the ingredients that make India such an exotic and colourful destination; just in a smaller dose.
The first time I went to India, I bought a cheap 14-day charter flight to Goa. Foolishly I took the bone-crunching overnight bus to Bombay. I spent one week in Bombay just sightseeing, enjoying the restaurants of Colaba and getting a sense of India. From Bombay I flew back to Goa, the flight was so short that I didn't even have time to eat the food served on the flight. My second week in India was spent lazing on the beaches. I didn't see much of India but this short trip gave me the confidence and desire to return for a much longer visit the following year.
It is also possible to find cheap charter flights to Kerala and to Agra.
Flying to Delhi is usually more expensive than flying to Goa. But, there are some good reasons for choosing Delhi.
Delhi is a tourist destination in itself and closer to many tourist destination in the north of India such as Corbett national park, the Taj Mahal in Agra, Jaipur, Rajasthan, Ranthambore national park, Varanasi and the Himalayas.
Flights to Delhi are usually on regular airlines such as Air India, KLM, Air France and British Airways. They offer more flexibility and tickets that remain valid for a longer period of time. With a regular airline you can return up to 3 months (or longer) after your outbound flight. With a charter flight you may have to return within 14 days after your outbound flight.
If you are planning to fly to/from south-east Asia (Bangkok in Thailand, Kuala Lumpur in Malaysia and Singapore) then you may find that flights to/from Calcutta are the best option. A popular route is Calcutta - Yangon (Burma) - Bangkok.
Calcutta is close to several popular destinations such as Darjeeling, the Sun temple at Konark, mountains of Sikkim, Sunderbans national park and Kaziranga national park in Assam.
If your main interest is southern India then a flight to Bangalore might be the best option. Bangalore is an expensive and over-developed city so rather than wasting your time and money, don't stay in Bangalore. Take a bus or train from Bangalore to Mysore, the journey is about 3 hours. Mysore is much more interesting and pleasant than Bangalore and has attractions such as the royal palace and Tipu Sultan's fort.
Bombay is the business capital of India. Consequently, hotels in Bombay are much more expensive than in other Indian cities. For this reason I think it is better to choose a different port of arrival.