I agree with WAMZ, Bishnupur is definitely one of the places that you should visit if you're travelling to West Bengal. The terracotta temples here are not only beautiful but so so ancient, you feel like you've been suspended in some sort of time warp, which is actually truly overwhelming.
Beside the obvious capital city Kolkata, you should also visit Shantiniketan. This is where Tagore established the Vishwa Bharati University. It's a place that is cocooned in the warmth of beautiful nature and culture that carries on the music, dance and literary traditions of the great poet, not quite modernized as the capital city and the home to a mind boggling variety of art and craft practices.
If you have time, you may want to hit the north and give Darjeeling a visit as well. Known as the "queen of hill stations" since the time of the British, this simultaneously sleepy and lively mountain town will take your breath away. If you can wake up early morning, you can catch the sun hitting the peaks of the Kanchenjunga (third highest in the world). It's a sight you wouldn't forget easily. Nearby is a sleepy spot called "Ghoom", a quaint town whose name literally translates to "sleep" in Bengali. This place has one of the oldest Buddhist monasteries in India housing some really ancient scrolls. If you wish, you can drive up another 5km up to Tiger Hill, which, on a clear day, offers a view of not only Kanchenjunga but Mount Everest as well.
Last but not the least, you can also visit the historical town of Murshidabad that still holds colonial architectural evidences of the Dutch, Armenians and the British. The famed Hazarduari (house with the thousand doors) on the banks of the Bhagirathi is one of the more popular tourist attractions here, although there are a few other palaces and ancient mansions that have now fallen from prominence.
Hope this helps!