I am going to Goa for business purposes for 15 days, and will hardly get 1 day free. What are the must-see places and must-do stuff in Goa? What should I be carrying along?
I am interested in Museums and Beaches and not clubs or strip-clubs.
Well Goa has an almost unbroken 70 km coastline of beaches, so I'd definitely try and fit that in at some point.
If you are after souvenirs, try the Anjuna flea market.
Sounds like you won't have time for diving or kitesurfing etc, so won't worry about that. However if you're at the beach you may see an opportunity for something like that or jet skis, or paragliding.
The Butterfly Conservation Project of Goa is a highlighted tourist attraction, open from 9am till 3.30pm.
Personally I can't go somewhere without trying the local food, and there it's the fish curry, especially the ones found in many beach shacks. Probably best to avoid the Vindaloo if you have a weak stomach.
I've been to Goa twice only, so I can't claim to be an expert. You haven't mentioned where you will be located, so perhaps what I'm going to write won't be suitable for you.
The first time I went north; we stayed near Mandrem, which turned out to be a very relaxing area to be, close to the more lively Arambol but with a nicer beach and fewer people around. I also appreciated the fact that you could easily reach Mapusa (where I liked the market very much) and Old Goa. I liked the colonial town, visited the various churches and cathedrals, which are so different from all the temples you normally visit in India.
I agree with Mark Mayo about the Anjuna Flea Market, which I consider an experience even if you don't buy much.
Last Christmas I went south; we stayed in Agonda, which is considered to be a wonderful location; it's true that the beaches in the area are quite large and the palm trees add to their appeal, but the area is too touristy in my opinion, and besides there is very little to do apart from lying on the beach.
I don't know how to answer your last question (what to carry along). I hope that what I've written so far may be of use.