The best and most convenient station to reach Palolem beach is Canacona. Please find some of my observations while I visited this station:
1. Palolem Beach (Pocket friendly hack): To save 1500 - 1800 rs of getting to the beach in a Taxi from Madgaon, use this station. There are some outsation trains which have a halt at Canacona(like Matsyagandha, Netravati and Gandhidham Nagercoil Express). If your train doesn't have a halt at Canacona but halts at Madgaon or Karwar, follow the below trick:
Look for a train that goes towards Karnataka from...
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Madgaon and halts at Canacona. If there isn't a train on the Madgaon - Karwar direction, get down at Karwar and take a train going towards Madgaon which halts at Canacona.
Eg: In our case, we booked 12133/Mumbai CSMT - Mangaluru Junction SF Express from CSTM to Udupi and got down at Karwar. Then we took 56640/Mangaluru Central - Madgaon Passenger from Karwar and got down at Canacona. Ticket cost: Just 10Rs per person from Karwar to Canacona.
Palolem beach is just 1.5 Kms away from the station and the best way to get to the beach or to a hotel closer to the beach is by walk. The autos charge Rs.100 from here to the beach.
2. NH 66: This station is very close to NH 66(Pnvel Kochi Highway). You will get KTCL, NWKRTC and variuous other public transport buses to Margao, Vasco and other parts of Goa and Karnataka from here.
3. Taxis/ Bike Pilots: We did not find any taxis at this station during our visit. Taxis would be available from NH66. No bike pilots are available at this station.
4. Bikes on rent: The closest bike rental is at a distance of 1 km away from the station, on the way to Palolem beach. The rates during Feb 2018 were 350 for an Activa/Scooty for a day, i.e 9 am to 9 pm. Do not pay any deposit. You need to keep an ID proof with them as a security for the bike. Do not keep your driving license. This is the best mean of transport for sight seeing.
5. Cleanliness: This is a very clean station with ample benches, watercooler and toilets, all available on PF 1. The ticket counter opens 2 hrs prior and closes 5 mins before a departure.
6. Places to Visit: a) Cola Beach: The best beach in Goa and infact in whole of India. You would be mesmerized by its beauty. There is sea on one side and a fresh water lagoon on the other side. We went there twice from Palolem on our rented scooty. The final 1.5 KM of road to the beach is very bumpy and requires some bit of offroading. After parking your bikes, you need to walk down about 50 steps to reach the beach. Distance: 12.5 KMS from Canacona.
b) Cabo-De-rama Fort: Known for the best views of the Arabian Sea, this is a fort which is covered by sea on three sides. A must visit place if you are in South Goa. Bonus Tip: After entering the fort, get down through the left side of the Church for some of the most magnificent sceneries.
c) Palolem Beach: A beach full of Shacks and Restaurants all over. Most crowded of all the South Goa Beaches but still beautiful than many of North Goa's best beaches. You can get a boat ride to Honeymoon Beach , Butterfly Beach and some Dolphin Spotting early morning. Distance: 1.5 KMS from Canacona.
d) Patnem Beach, Agonda Beach, Galgibaga Beach : Some of the other beaches which are less crowded and pretty.
e) Mallikarjun Temple: On the way to Galgibaga Beach on NH 66.
South Goa is the place to be in if you are looking for peace and serenity with clean beaches to stroll around.
Have a safe trip.

Please update new time table to reflect Manugur origin....
Train Number Train Name From Station Destination Station Runs From Source On
11303 MUGR KOP EXPRESS MANUGURU C SHAHUMHARAJ T MON TUE WED THU FRI SAT SUN
SNo Station Code Station Name Route Number Arrival Time Departure Time Halt Time(In minutes) Distance Day
1 MUGR MANUGURU 1 -- 15:30 -- 0 1
2 BDCR BHADRACHALAM...
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RD 1 16:30 16:50 20:00 50 1
3 DKJ DORNAKAL JN 1 18:03 18:05 02:00 104 1
4 MABD MAHBUBABAD 1 18:19 18:20 01:00 128 1
5 WL WARANGAL 1 19:28 19:30 02:00 189 1
6 KZJ KAZIPET JN 1 19:50 19:52 02:00 199 1
7 ZN JANGAON 1 20:37 20:38 01:00 247 1
8 BG BHONGIR 1 21:09 21:10 01:00 284 1
9 SC SECUNDERABAD JN 1 22:55 23:10 15:00 331 1
10 BMT BEGAMPET 1 23:20 23:21 01:00 335 1
11 SNF SANAT NAGAR 1 23:27 23:28 01:00 339 1
12 LPI LINGAMPALLI 1 23:44 23:45 01:00 353 1
13 SKP SHANKARPALLI 1 00:04 00:05 01:00 374 2
14 VKB VIKARABAD JN 1 00:30 00:32 02:00 402 2
15 TDU TANDUR 1 01:00 01:01 01:00 444 2
16 NAW NAWANDGI 1 01:24 01:25 01:00 461 2
17 KQT KURGUNTA 1 01:34 01:35 01:00 469 2
18 SEM SERAM 1 01:44 01:45 01:00 477 2
19 MQR MALKHAID ROAD 1 01:54 01:55 01:00 489 2
20 CT CHITTAPUR 1 02:24 02:25 01:00 499 2
21 NW NALWAR 1 03:01 03:02 01:00 528 2
22 YG YADGIR 1 03:28 03:30 02:00 553 2
23 SADP SAIDAPUR 1 03:49 03:50 01:00 576 2
24 KSN KRISHNA 1 04:18 04:20 02:00 596 2
25 RC RAICHUR 1 04:48 04:50 02:00 622 2
26 MALM MANTHRALAYAM RD 1 05:19 05:20 01:00 650 2
27 KO KOSGI 1 05:29 05:30 01:00 663 2
28 AD ADONI 1 05:58 06:00 02:00 691 2
29 GTL GUNTAKAL JN 1 07:20 07:30 10:00 742 2
30 BAY BALLARI JN 1 08:45 08:50 05:00 793 2
31 DAJ DUROJI 1 09:19 09:20 01:00 820 2
32 TNGL TORANAGALLU 1 09:29 09:30 01:00 825 2
33 HPT HOSAPETE JN 1 10:08 10:10 02:00 858 2
34 KBL KOPPAL 1 10:38 10:40 02:00 886 2
35 GDG GADAG JN 1 11:38 11:45 07:00 943 2
36 UBL HUBBALLI JN 1 13:20 13:30 10:00 1001 2
37 DWR DHARWAR 1 14:05 14:10 05:00 1021 2
38 LWR ALNAVAR JN 1 14:49 14:50 01:00 1058 2
39 LD LONDA JN 1 15:38 15:40 02:00 1092 2
40 BGM BELAGAVI 1 17:03 17:05 02:00 1143 2
41 GPB GHATPRABHA 1 18:28 18:30 02:00 1201 2
42 RBG RAYBAG 1 18:59 19:00 01:00 1230 2
43 KUD KUDACHI 1 19:19 19:20 01:00 1247 2
44 MRJ MIRAJ JN 1 20:35 20:50 15:00 1280 2
45 HTK HATKANAGALE 1 21:19 21:20 01:00 1306 2
46 KOP C SHAHUMHARAJ T 1 22:40 -- -- 1327 2