Myeik Airport (MGZ) serves Yangon, Kawthaung and Dawei. (There are no flights to Mawlamyine.) APEX and KBZ run the flights, with KBZ prices being consistently slightly higher. Flag carrier Myanmar National Airlines also flies to Yangon.
As of February 2016, APEX flies to Kawthaung on Monday, Wednesday and Friday for $55 and KBZ (daily) charges $72. APEX is $65 to Dawei (daily). Yangon is $85, $100 and $120 with APEX, KBZ and Myanmar respectively. Any hotel or travel agents will be happy to check current schedules for you and reserve tickets.
The tiny airport is close to the town centre and while hotels will arrange transfers for you a tuk tuk or minivan will set you back 1,000-2,000 kyat.
A minibus to Dawei is 12,000 kyat while an air-con bus is 8,000 kyat; the latter continues to Mawlamyine for 18,000 kyat and Yangon for 20,000-25,000 kyat depending on the company. It takes around six hours on a reasonable road to Dawei, while Mawlamyine is 13 to 14 and Yangon at least 20 or so. Kawthaung is 25,000 kyat by either air-con minibus or large bus; fan buses are 15,000 kyat. All take at least 12 to 14 hours.
A proliferation of companies offer services and all have varying (and frequently changing) departure times. Transport company offices are found along Baho Road plus your hotel will be happy to book for you for a small commission. Each office tends to sell only tickets on their own buses and hotel receptions tend to have deals with only one or two operators.
Jade Flower Travel, downstairs in Grand Jade, do cover a fair number of options. They have English speaking staff though they do whack on a bit more commission than usual. (They gave us dollar rates and suggested either a 05:00 minibus at $13 or 18:00 air-con bus at $7 for Dawei, for example.)
As of early 2016, public boats between Kawthaung, Myeik and Dawei are not running.
Most of central Myeik is small enough to be walkable though plenty of cheap public transport options are around. There’s the usual motorbikes with side platform attached, which function as the town’s tuk tuks as well as plenty of motorbike taxis and the ubiquitous little two-bench minivans for larger groups. Around town fares shouldn’t be more than 500 to 1,000 kyat while the airport is 1,000-2,000 and the more distant bus station 2,000 kyat.
Jade Flower Travel provide motorbike rental. Manuals cost 6,000 kyat half-day, or 10,000 for a full, while an automatic is 8,000/12,000 kyat. Sun and White Pearl Guesthouses also offer motorbikes for 7,000-8,000 per day (though the motorbike shop next door to Sun will do it for less). Unlike Dawei or Ye though, there aren’t too many spots outside of town to visit with Tanintharyi being better explored by boat. Note that also compared to other southern towns Myeik roads are busy!
When in town we used a very helpful and obliging moto-taxi driver with good English by the name of Htay-Oo (Tayo): (094) 2070 6552.