Budget hotels and guesthouses can be found everywhere. Even in the touristic places the budget hotels are very cheap. This also includes breakfast. Remember that the government cuts down power supply every day for a couple of hours, so your AC might not work for some time unless the hotel has its own generator. Always have your torch or candlelight ready.
Hotels can only accept tourists if they have a permit.
The permit is usually exposed behind the desk. Take care, because people can get in trouble for giving you lodging without having a permit. Prices of hotels in Yangoon are more expensive. The people in Myanmar are extremely friendly and polite. So for the tourist, it is a very safe country.