If you come and stand on the Calangute beach in Goa and face the ocean, there are two treks that you can do - one to your left, the other to your right. Both treks are very different, but undoubtedly and exceptionally beautiful. I'm going to talk about the one towards the right, which will take you through beautiful beaches like Calangute, Baga, Little Baga (did you know this beach exists?), Anjuna, Vagator and all the way uphill through a dense jungle to the Chapora Fort. before you embark on this trip, I suggest you print a map of North Goa and keep it with you. Please do not refer to it just now, just keep it with you. You'll refer to it when the time is right.
Turn right from where you were facing the ocean in Calangute, and start walking along the shoreline, keeping the sea to your left. Wet your feet, splash water on your girlfriend, hold your spouse's hand, show tiny crabs to your kid, and reach Baga in around half an hour. When you reach Baga, it may seem to you that your path has been cut off by a channel of water that connects inland drains to the sea. Don't get disheartened. That lovely green hill that's beckoning you will have to wait, but only for a little while. Turn right and dissect the shacks into the Baga village and let your biological compass find a bridge that takes you across the channel and at the foot of the hill. The real fun starts here. In the monsoons, trekking along the ridges of the hill could be a little dangerous, but with proper hiking shoes, and a stick to clear away bushes from your path, you will be just fine. Rise up the ridges and when you reach the top, you'll see a sight that 99% of the tourists would not be able to see. Behind you, is a vast green plateau, which will cure your eyes of years of exhaustion if you keep staring at it for 10 minutes. In front of you, the majestic Arabian Sea lies in all its glory, reminding you with every crash of the waves on the rocks down below that there are things in this world that are way, WAY larger than what we consider important in our day-to-day lives. Sit there for some time, and then descend the hillock to reach one of the best kept secrets of Goa - a secluded little beach called 'Little Baga'. There's just one shack there, and hardly a couple of hundred feet of beach, and chances are - you'll be the singular soul on that beach. The beach itself is nestled right in the middle of green hills on three sides, and the ocean on the fourth.
After you've celebrated your solitude in whatever way you may deem fit, start climbing the hills again, ocean to your left. This climb is a treacherous one - drink a lot of water, and watch your step. 'Pugdandis' or walking paths will be your best guide, but not always. There are a lot of cashew plants around, so be careful of straying animals, like bears. Keep walking, make sure your biological (or phone's) compass is always on. Keep moving north. The ocean should always be on your left. Make your way through the hilly terrain, and reach a rocky descent down onto what I call a 'relief' after the treacherous hike - Anjuna beach. I've done this trek at least 5 times, and on all occasions, the moment I climbed down to the Anjuna beach, I just dove into the cool and refreshing water. I can't explain the beauty of that experience in words. You are back in civilization again, so you'll find a lot of shacks lining the beach. Relax, doze off, have lunch, solve Differential Equations, and pat yourself on the back for having made this far.
Then, pick yourself up, because, believe it or not, you've not even covered halfway. Keep walking along the beach and reach the famous Anjuna Flea Market. The market is open on Wednesdays, and you get some good stuff there. From here, I recommend walking through the asphalt road and going towards the spot where all the buses drop off the tourists. Your target should be (once again, and bravo!) the hill right in front of you. Find your own way to the foothill and start climbing once again. Reach the top, and you'll realize that this is a much greener plateau than the one you had seen a few hours ago. Keep going, there are no specific directions, except that you need to keep moving north, with the sea to your left. You'll go up and down and up and down in a rollercoaster of greenery, and then finally, you reach a sheer drop. Start climbing down. Be VERY careful here, it's not as easy as it seems. Your objective will be to reach the Vagator beach that you can see down below, between the swaying palm trees. Reach Vagator and take a short break. Vagator's sand is quite hard, as compared to that of other beaches, making it easier for you to walk. Keep walking, and when you can't go any further because of razor sharp rocks jutting out of the water, look up to your right, away from the ocean. That's the hill you need to climb to reach the 'Dil Chahta Hai' fort - Chapora. Once again, it's a steep climb, almost impossible if you don't have the right gear, or are tired, or hate gymming. But if you have the spirit in you, you'll be able to do it. Once you have conquered the fort, I suggest you refer to the map you had printed and kept in your rucksack earlier. Find Calangute, find Chapora fort, and say to yourself - If I can do this, I can do anything.