Western Myanmar is a region of Myanmar.
The simplest way to get to the Rakhine region is to fly from Yangon to Sittwe (IATA: AKY). As with all domestic flight schedules these can be erratic so try to give yourself some extra time on either end for connections.
Thandwe Airport (IATA: SNW)
Renting a private boat and guide to get up the Kaladan River to Mrauk U and points further is not too expensive and makes for a very interesting trip.
There is some concern about being on the Kaladan River after sunset, purportedly due to the danger of being robbed.
In 2016-17, there was a widespread campaign of murder and rape of Rohingya people, torching of their villages, and forcing them to flee from Rakhine state. As a result of this and conflict between Rohingya forces and government forces, there are travel advisories. For example:
The UK Foreign and Commonwealth Office (FCO) advise against all but essential travel to Rakhine State except the southern townships (administrative areas similar to a borough or county) of Kyaukpyu, Ramree, Munaung, Toungup, Thandwe (including the tourist resort of Ngapali) and Gwa.
http://smartraveller.gov.au: Rakhine State (except resort areas at Ngapali Beach); Northern and Central Shan State, Kachin State, reconsider your need to travel
Government of Canada: Avoid non-essential travel to the following states, due to the risk of serious civil unrest:
Safetravel (New Zealand): There is high risk to your security along the borders with Laos, Thailand, India, Bangladesh and China and it is advised against all tourist and other non-essential travel in the vicinity of these borders, including official border crossings. Military activity, ethnic militias, armed drug smugglers and the presence of landmines pose a particularly high risk to your safety.
There is high risk to your security in Kachin State (excluding Myitkyina), the northern Rakhine State areas of Maungdaw, Buthidaung and Rathedaung, northern Shan State and Paletwa township in southern Chin State due to ethnic tensions and the potential for armed conflict and violent civil unrest. It is advised against all tourist and other non-essential travel to these areas.