Tarkarli is definitely "the" place to go. The MTDC cottages and facilities are superb. Although I went 6 years back, I hope it is still as good.
Buses go to Malvan (only 6 kms away) from Mumbai but I won't recommend that. It's slow and uncomfortable. It started from Borivali at 3 and was still in Mumbai by 7 pm. If I go again (and hopefully I would) I will take train both ways.
I recommend taking the train to Kudal which is nearest train station ( The Konkan rail route is stunning.) and then take an autorick to Malvan or direct Tarkarli.It's about 40 km or 1 hr away drive/ride.
Check out the trains online on Indian rail site from Mumbai to Kudal. We took an overnight train for return journey but I believe even Shatabdi from Mumbai to Goa also stops at Kudal which could be convenient. about 10 years ago