Dawei (Tavoy) is the capital of Tanintharyi Division, in Southeastern Myanmar. As this area has been closed for tourism until early 2013, it is largely undeveloped and unexplored and makes for a very authentic and rewarding experience. Don't expect to find any packaged tours or trips yet.
Air KBZ has daily flights during tourist high season (beginning October to end of April) which fly from Yangon to Kawthoung (and return) stopping in Dawei and Myeik. Myanmar Airways flies twice daily from Yangon, once direct (1h) and once with a stop in Kawthoung (3h).
There is one daily train from Yangon to Dawei via Mawlamyine and Ye, which takes just over 24 hours. It departs Yangon at 18:25, departs Mawlamyine at 04:30, departs Ye (where you change to a different train) at 10:25 and arrives in Dawei at 19:00 (at least according to the schedule - delays are common).
Ferries to Myeik and Kawthoung leave from about 35km (21 miles or about one hour's drive) south of Dawei at around 04:00. You will need to be at the jetty by 03:00 as they will leave early if possible. It takes around 4 hours to Myeik (USD25-30) and about 10 hours to Kawthoung. The coastal ferry does not operate during the rainy season.
There are plenty of pickups, motorcycle taxis and trishaws in town to comfortably get around for just 500 to 2000 kyat. Another option is to rent a motorcycle and go around at will, most hotels can arrange one for 7000-10000 kyat a day.
Please dress modestly (cover shoulders, knees etc) in temples and pagodas
It is very easy to get to the beach at Maungmagan, it takes about 30 minutes and during high season there are many restaurants at the beach that serve excellent seafood dishes. However, first check the kitchen of the place you want to sit down at. A little rougher is continuing north on the road towards Nabule. It soon becomes a dirt road and requires better bike handling skills. A few kilometres before Nabule there is a straight pebble road to the left, which will take you past the (seemingly abandoned) Dawei Sea Port project site, towards a giant undeveloped beach. Really tough and adventurous is going to the south, and taking a dirt road westwards out of Langlon. These 'roads' are rocky, steep and require top motorcycle skills to navigate. At the end you will find different beaches where only a few curious local fisherman families reside. They will gladly invite you to take a swim with them. There is also a path towards a small empty beach and a golden rock. From Launglon, take the first intersection left, then a few km further continue straight when another path goes left up a hill, and park your bike at a little shrine at a 3 way intersection. From there take the path to the right that leads up (not the smaller one going down), cut through the fresh overgrown bushes to the end, and climb the rocks to the golden rock with the Buddha statue and on towards the beach. Study satellite imagery beforehand to prepare for the trip.