You can't rent a car in India yet. You have to hire it with a driver and it is quite inexpensive considering that the driver can be available for up to 18-20 hours, if you want. Driver are always willing to help you in anyway they can. Treat him well, give good meals, a nice tip Rs. 500 ($12-14) and he be willing do almost anything for you.

If you are more adventurous try the Motorcycle on rent. You can either rent it or get a driver to give you a ride.

There are some real old churches in Goa which you might wanna see. If you are devout Christian then body of Saint Francis is kept in one of the Churches and is still in a very good preserved state. There are also some very old temples in Goa (the ones which could survive the onslaught of Portuguese). You can see them too. Aprt from these there are some forts and a lot of beaches.

Goanese cuisine is quite popular for its sea food and curries. Being a vegetarian I haven't really tried it much but "Vindaloo" is supposed to be great.

I would also recommend winter months when weather is quite pleasant except December when everything is fully booked and prices are 2-3 times the usual rates.

If you are a female except southern beaches, at all other places dress casually and wear lose cotton cloths that keep you cool and don't show too much skin and you should be fine.