Southeastern Yunnan is in China.
The old narrow-gauge railway linking Kunming with Hekou on the Vietnamese border sees no passenger service along most of its length. However, a new standard-gauge railway has been completed in the early 2010s between Kunming and Hekou. Stops include many of the southeastern Yunnan cities: Yuxi, Tonghai, Jianshui, Mengzi, Hekou. There are about half a dozen trains a day in each direction on the Kunming-Mengzi section; fewer, south of Mengzi. Most of the train stations on the new railway are a fairly long way out of the towns they serve, but local bus service between the station and the town is usually available.
Mengzi has an airport as well.
Trains can be used to move between the cities on the new (standard-gauge) Kunming-Hekou line (via Kunyang, Yuxi, Tonghai, Jianshui, and Mengzi). Thanks to extensive tunneling, the railway is straighter than most roads, which makes a train trip faster and more pleasant than one by bus. Note that in most cities, the train station is quite a way out of town, but bus service to central city is usually available.
There is a century-old old narrow-gauge, 100 km or so to the east of the new standard-gauge line, but it has no passenger service.
Buses can be used to travel everywhere else; Mengzi is the region's main hub.
Traveling by bicycle in SE Yunnan is possible, and often quite rewarding. Most cities are within a day's trip from one another (60-80 km) along a provincial highway (省道). As cities are usually in river or lake valleys, riding between two cities will involve climbing at least a couple of hundred meters, and then losing elevation.
The Red River flows in a narrow and deep valley, about 1,000 m below the towns north or south of it, so all the roads descending into it have an impressive series of switchbacks.
Be aware of the combination of the usual hazards of riding in China. When crossing industrial/commercial suburbs of most cities, you'll go through a belt of congested roads, smoke and dust. Once outside of the densely populated area, the traffic is usually low, but the road may have some sections being repaired - or in dire need of repair.
Locally produced tropical fruit are available in the southern part of the region. Try local bananas, jackfruit, passion fruit, loquats, and even mangoes. Strawberries are grown in large fields in the northern counties of the region, e.g. around Yuxi.