This article is a travel topic
The Painted Monasteries are in the southern Bucovina, in northern Romania. Most of them have been nominated World Heritage site by the UNESCO. They are all in very isolated places surrounded by farms and a nice countryside. If you see a map, most of them will be located next to a town with the same name, but this doesn't always happen. The truth is that several houses were built next to the road leading to these monasteries, but they are all farms and these "towns" have no center, no public transport, so I would hardly call them towns. They are all very beautiful but very small so, if you just want to see the monasteries, it's not worth spending more than one hour in each place.
There are guides offering tours of the Monasteries, just search online and contact them beforehand. English is widely understood and spoken in Romania and hitch hiking is common among locals, often giving the driver some money for fuel costs. It's an easy and safe option to travel, often more convenient than public transport. Renting a bicycle to visit multiple monasteries starting from Gura Humorului is a great option for active travellers. Renting a car to wander around can be an alternative: in 1 or 2 days you will be able to enjoy every place properly.
If you want to take your time and walk around enjoying the beautiful Romanian countryside, then you might consider spending more time there. Finding a place to sleep will not be a problem: lots of houses rent a room to tourists, see ruraltourism.ro for example. If you go to Gura Humorului or Suceava you can find good quality hotels for very reasonable prices. Getting inside the Monasteries will cost you 5 lei; if you want to take pictures you are supposed to pay an extra 10 lei (2016 price). Never are you allowed to take pictures inside a church.
Please note that most of them are currently being renovated in the inside, but visiting is still possible and definitely worth it.
The closest bigger city is Suceava. There would be a bus connecting the Monastery to the city, but it passes only twice a day, in the early morning (about 7:30) and late evening (about 9 pm). It is better to use the taxi; tell the driver to use the taximetru set to 1.5 lei/Km (the standard price there to go outside the city). In Suceava, you find taxis in the center; ask them to leave you their number and, if you are in the Monastery, you can ask the nuns to call it again for the way back. The monastery is very beautiful, even if it is not painted outside like the others. If you want you can remain to sleep at the monastery. They will give you a room in a small building next to the monastery; it will cost you 50 RON/night for a double room with private toilet. You can go to eat inside the monastery, they will offer you this choice if you decide to sleep there. You haven't got so many chances because there is no other place to eat around, but it's worth trying: the breakfast is 15 RON/person and the meal 20 RON/person, but most of what you'll eat is made with the local products by the nuns.
It is 6 Km away from Gura Humorului. You could consider going there walking from there, it will take about 1 hour and half. There is a minibus leaving from the Best Western hotel to Humor and back very often, and it will cost you only 1 leu.
The monastery and its garden is very nice, it has a much better, tranquil atmosphere than Voronet. Moreover, there is an old watchtower where you can climb up for sightseeing.
The monastery is surrounded by huge walls and towers, and is located outside of the settlement. The paintings are also very nice, and it has (unlike other monasteries) a small museum as well. Also, it has a computer with English language content telling everything about the monastery (including local stories not found in other travel guides).
Moldovita lies up in the mountains, approx. 30 min away from Sucevita. The monastery also has a nice garden filled with roses. However, it is smaller than the other monasteries.
There is no public transport going to Voronet, so you have to take a taxi, go with a planned trip or simply walk down the main road till you see the sign and hitch hike there: everyone here goes there. A possibility to be considered is to go walking from Gura Humorului: the landscape is very nice and the street is about 4 km, so it will take about 1 hour to get there.
Currently (July 2012), a building it being built right next to the monastery. This monastery, unlike the others, is very touristic because this is the most famous from all of them. The reason for this is the famous Voronet blue used in the frescos, which is unique to this monastery. The place is well worth a visit.
For entering the monastery, you may be asked to wear special clothes (no shorts or t-shirts are allowed); however, this kind of requirement does not exist in the other monasteries.
External sources of information
Some external websites have more practical information for visitors, like romaniatourism.com, http://www.discoveringtransylvania.ro/tours/painted-monasteries-in-bucovina or more detailed information about each monastery's history like wikipedia.org