How can I choose a good destination to see whales, especially blue and humpback, preferably from a boat?

Whale watching is possible in many spots around Australia as well. Western Australia is relatively close to you and they have (depending on the season) both humpback and blue whales.

Baja California is probably one of the best location since the whale migration is very predictable there because the weather tends to be quite consistent from year-to-year.You can get extremely close to the whales and even see new born whales. Check this tour's info for example.

Quebec has a location famous for whale watching called Tadousac. It is about 5 hours drive from Montreal, although if you can land at Quebec City, then its only a couple of hours. You have to time your visit carefully though, I think early August from what I recall. Here is some info.

There are also whales which pass near the coast of Ecuador. I saw a few - but fewer than at the other locations - on a boat trip to Isla La Plata. This is a relatively cheap trip. I don't remember though if the whales there arrive seasonally. Basically our boat went out and the captain went in different directions until we encountered some whales. Seas are rough there though, so I got very sea-sick, but others had no issues.

The gray whales perform their annual migration from Alaska all the way down to Baja California Sur, i.e. along the Pacific Coast.

I had the opportunity to make a trip to San Ignacio Lagoon, Baja California Sur in Mexico several years ago. This spot is well-known to be a "nursing" spot for the gray whales. From January to April you are very likely to encounter one of the newborn gray whales from up-close in their natural habitat.

They took us on a really small boat (like a dinghy) and waited on the lagoon instead of chasing after the whales. Eventually, a small whale approached our boat and actually let us touch it. Meanwhile, the larger mother whale waited patiently from a distance. We got to see and touch at least 3 of these whales.

If you want more information on this specific spot, google "Ecoturismo Kuyima", which is the company from which I booked this trip. They offer eco-tourism style accommodation on the lagoon and handle the boat trips for a really cheap price.

On your budget, I am sure you can find a cheap flight to Los Angeles, and then make a road trip down the coast to Baja. You will get amazing views on this scenic road.

Alternatively, if you prefer blue whales, you have Sri Lanka very close to you. Take a flight to Colombo and then drive down to Mirissa Beach. From there you will be able to arrange a boat trip to see the blue whales, although from a much larger distance (and probably less time) than what you would get in Baja with the gray whales.

Stellwagen Bank is probably one of the best whale-watching locations in the continental United States. Whale-watching tours depart from downtown Boston, as well as from some smaller towns that can be reached easily via public transportation (Gloucester and Provincetown).

The advantage of this location is that it is also relatively close to a major international airport (Boston Logan); while there are no non-stop Bangalore-Boston flights, there are about a half-dozen ways to make the trip using only two flights. It is then relatively easy to reach the embarkation point for the whale-watching without the use of a car.