Kaili is on a railroad line connecting Kunming and Changsha. You could get a train from either of those, or from Guiyang.
There are also various festivals. The rain-worship ritual is held on August 5th of this year in the south of Kaili. There you will see traditional rain-worship, Dong people's music, singing and dancing under their Drum towers, indigo-dyed pleated skirts and festival jackets with silver ornaments. During this summer time, it is a short free time for the work in the fields, locals of Miao and Dong will arrange bullfights and some more festivals, such as Eating-new-rice festival. This is held almost everywhere in the south of Kaili.
Travel agencies or hotels can arrange trips to touristic village such as Nanhua, Langde, Xijiang and Zhaoxing, or if you're feeling adventurous and speak some Chinese, you can get there more cheaply by local bus.
"Lang De Miao village". A bit touristic, but very nice location and higher part of the village is quiet. Go there via Lei Shen and visit the market there.
Also Xijiang, the largest Miao village, is not far away, or go to Datang, with its store houses on pillars in water basins.
"Chong An Jiang village" with its picturesque waterfront. Pay 1Y for the ferry to the other bank for a great view.
"Zheng Man Dong Miao village", famous for its Batik works.
The two old towns close to Geyi (~3km); take the bus to Geyi and than a taxi from Geyi or walk.
Leishan, 40km south, a small city with few minority ethnic groups and nice buildings. Better place than Kaili to stay overnight.