Depending where you stay in Goa you must visit as far North and South as you can as the beaches are all so different - hire a taxi by the day which usually costs between £10 (from North) to quite a lot more in the South (as discovered in December 2008)when the driver tried to charge almost £30 for a 4 hour trip to the North)  if you take the trouble to chat to your driver they very often end up being firm friends and as good as any guide. Most taxis in the South are linked to the 4 and 5 * resorts and their prices reflect this, . If you can find and independant driver you will get prices that are far more realistic. Visit Old Goa and the wonderful temples just outside Ponda followed by the spice plantation. As the spice plantations are shady they are usually nice and cool and after all that wandering around the temples and buildings are a pleasant change. Look out for the kingfishers diving into the ponds for fish and paraqueets flying free squaking as they go

Spend an evening going on one of the local sunset/moonlight cruises on the Mandovi river costing a little over a pound and if you get on the right boat (with the most locals and the noisiest music) you will see the Indians enjoying their Punjabi dancing with the occassional European tourist trying to compete. That takes approximately one hour. Then as you are in Panjim head to one of the fabulous restaurants such as the Dehli Darbaar  or the Quarterdeck. Of course if you are a gambler there is also the floating casino boat Carvella where you can gamble eat and drink. 

There are lots of tourist markets springing up everywhere now but the old favourites Anjuna on a Wednesday and Mapusa on a Friday are still great fun. The local markets are also great fun and talking to the spice girl(sellers) and haggling for the prices can be an enlightening experience.

The beaches as previously mentioned are beautiful so much of your time will probably be spent on them, most beaches have shacks (temporary bars/restaurants) where the food and drink is fabulous and also cheap, get to know you shack owner and his staff and you will never be forgotten, they remember you from year to year!  Keep your eye on the sea and the chances are you will see the dolphins jumping and putting on a free show. No need to go out on a boat unless you really want to. Watch out for the sea eagles overhead also.

Depending on you personality and the time of the year, the things one wants to do can vary greatly. In monsoon, especially, several things that Goa is known for (the rave parties, the beach shacks, the flea markets) are all but closed. But, nevertheless, having all of Goa just to yourself (very few tourists) and the flexibility to do your own thing can prove to be just the right thing to do in Goa.