Sri Lanka would be a good option. Kandy and Colombo are relatively safe right now (although one never can guess where the LTTE would strike next.)
If you are sticking with the cities you have mentioned, bear in mind that Delhi and Pune will be very cold, between 0-5 degrees celsius(which may not be too much for you, but thats cold by Indian standards.)
Calcutta is very crowded and moving from one place to another can take for ever but if you are ok with that
then you can check out the most visited spots -the Howrah bridge, the Victoria memorial and the botanical gardens. Some other spots of interest are the marble palace, Fort William,writer's building,etc. If you have a sweet tooth, you can try out the various milk based sweets the city is famous for.
They say Mumbai always evokes a strong feeling in the visitor- either love or hate but never indifference. You of course will be the judge of that in a few days. Wish I could have shown you around, but am neck deep amidst many unfinished projects right now. You can check out the Gateway of India( beware of drug peddlars and gigolos in the evening) If you're into ancient sculpture, the Elephanta caves might be the thing for you. You can check out paintings at Kala Ghoda. (The Prince of Wales museum is nearby as well.)
At Borivali, you can check out the National Park, although winter might not be the best time to visit.
The gay scene is as underground as it gets and very risky. So no recommendations regarding a regular gay club, coz there isn't one. Just secret parties.
cannot think of anything else right now. Hope you enjoy my city and my country.