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.