As well as Daytripper in Calangute have a look in Johns Boat Trips based in Candolim near the crossroads, and check out the trip to Devbagh Island. This is a really quiet place, after being transfered by 4 wheeler or mini bus you get to the island via a motor boat. You can either book huts on stilts or small cottages. These are all set in shaded trees with hammocks to laze away in or you are just 50 yards away from a clean beach with plenty of free sunbeds and a very calm sea. You have all you want in the accomodation - decent clean beds, hot showers, ceiling fan etc.. Food is buffet style, which was ok but could have been better (if you are 'picky' take some snacks with you as there are no shops at all. Plenty of drinks available also.
We were picked up early morning and were unpacked by lunchtime, so a decent afternoon to chill out. This was then followed by a small BBQ around 6.00pm with a great sunset in the background. At 8.00pm the buffet was opened and the rest of the night is up to you (sit back and chat with others over a drink). Could have done with more than 1 night here.
Another place that is right at the top of our list is Cola Beach, the part we were in consisted of 'Arabian style' tents - excellent.
Again, these were set just away from the beach in shaded trees. An early morning pick up gets you there for mid-day. Buffet style food again for evening meal and breakfast (better than Devbagh), and a few snacks available if needed. Excellent beach and clean sea, with a short walk to the next set up called The Blue Lagoon (I think this is where most people get placed, as where we stayed is supposedly set up for tour operators only). After an evening meal, the camp fire is lit and you get the locals putting on an impressive dance show (about half hour). This is the place to go to, and one I would defo reccommend for more than 1 night if you have the time.
Palolem (as mentioned by others) is one I wouldn't rule out to visit again, but sense that it is now getting like the beaches in Candolim/Calangute with beach sellers hassling you (maybe this has changed ?). I thought the huts on stilts were great fun and a nice set up. We stayed at the Cuba Beach Shack - along with all the others they have accomodation surrounding the main beach shack, but with communal toilets and shower rooms (I gave an impressive display when I didn't realise the door had come off the latch and was soaped up with a crowd watching !!) Food came off a menu, eat what you want, when you want. A small village with a main road leading down to the beach area had quite a few places to eat and shop for nic-knacks. It was busy when we went with a mix of Brits, Germans, Australians and a few Americans. Great time had by all, and a nice get away for a change of scenerey.
I think Big Daddys in Candolim own the Cuba so call in and see them to book it. Other than that, make your own way there and stroll down the beach - plenty of shacks with huts to choose from (some looked better than we were in with private toilet/showers).
Top of my list though - Cola Beach.
Spike.