accent is a hard one to improve, but not impossible. It just takes practice. What I have found with many Indians, is that what affects their accent the most is that they are used to speaking so fast in for instance Bengali, that when they speak English, it is far faster than I speak! :D
It was funny. One of my high school friends is Bengali, but was mostly raised in Australia. His Bengali is good, but people think he is "slow" because his speech is so slow to them. But in English, it is like he is speed rapping.
He owns a law firm now :)
My father had almost zero accent. What he did was slow down his speech and really concentrate on getting the sounds correct, before speeding up a bit again. But never as fast as when he spoke Bengali.
Now that you mention it, I realize that we do speak quite fast, especially when speaking in Bangla. Wow! Took me that many years to realize it, after a little side by side comparison. I'm Bangladeshi btw.
I have quite a few friends who've settled down in Australia after finishing up with their higher studies, it's been a decade almost. A few family members and relatives live there too, but most of them are in Melbourne.
I was supposed to move there as well, Sydney was the city I chose, but after facing some family and financial problems I decided to stay back and do what I can over here.
That's actually the correct way to learn I guess, and it sounds a lot more mature too. We should really take our time when we speak, no matter what language it may be.
Was your father Bengali?