There is less crowd in goa in rainy season... I did my engineering from sindhudurg district (mumbai uni) . Goa was hardly 1 and half hour from our college, we used to go to goa in rainy season mostly because everything right from bike rent, hotel lodging and food, cruising costs less in this season. We use to spend the saved money (just to call it so, actually it was more than what we spent on delicious goan food) on liquor. We used to stay at panjim in lake view resort, lake view colony (it was a resort(precisely a lodge), in which there were four rooms and kitchen, open terrace attached, all this at rs.1300 per day(we used to be 8 guys), and moreover the owner stays with his family on first floor and had two daughters (both seemed teenagers), we got dragged in the resort just by getting a glimpse of them

.. Bike rent varies depending on the CC of the bike, starting from rs.130(negotiated for passion plus, fuel was to be filled by us), similarly we took FZ, avenger etc, those bikes were negotiated at rs.180 per day basis. In North goa, you will find all beaches. In south goa, you see many churches,temples, museum, also some nice beaches like vasco, colva, candolim etc. all white sand beaches. WE also used to stay in VINCY resort colva,right in front of colva beach,awesome place, rs.500 per day per room, negotiated to 3 person per room, 4 werent allowed, swimming pool attached (useless as it was raining)...
NOw if you are travelling by road, i recommend you to first visit goa and then while travelling back you can enjoy the konkan region. Konkan has also got good beaches like kunkeshwar, bhogwe (known for dolphins), tarkarli(starfish and jelly fishes can be seen), ganapati pulay( known for temple of lord ganesh) etc, but who will bother to visit those beaches after visiting some many beaches in goa. You can go to marleshwar while returning to home, its a nice place, lots of biggie waterfalls and a temple in which snakes crawl around you but dont harm you. Then kashedi ghat has some good points, i dont remember the names, maybe the person driving would be knowing more. Thats all n mumbai-goa trip via mumbai-goa highway. I have not included mumbai-pune-kolhapur-goa highway. Enjoy