Is it possible to visit Old Goa (for a day trip) from one of the beach resorts? How long would a taxi drive take and how much would it cost? Or is it better to spend a night or two in Panaji, and then move to the beach?
Yes. I recently stayed at Calangute beach and a taxi driver took me to Old Goa and Panjim for 1400 rupees. This price is from a government table and is used by all the taxi drivers. If Panjim was not involved the ride would have cost around 1000 rupees. If you negotiate you can get it cheaper than the table price.
I don't remember exactly how long the journey took, but it was certainly not more than 90 minutes.
Your question is old but this answer might be useful to other users.
----> Instead stay where you are living, take a bike on Rent it would cost you from Rs. 150 to Rs. 600.00 or 700.00 per day depending on bike.
If you take a bike on Rent, few precautions: