Central Inner Mongolia is in China.
Chifeng Yulong Airport (CIF IATA), Tongliao Airport (TGO IATA), Xilinhot Airport (XIL IATA).
The train network covers most towns and cities even in remote parts. And if there are no trains, there are always buses.
One possibility is to try a Mongol homestay. But be careful. Sometimes, "Mongol homestay" may just as well mean "sleep in a plastic yurt with Han-Chinese package tourists" as actually staying with a Mongolian family. Actually, it is probably more likely to end up in a fake homestay than a real one if you don't use a reputable operator or get lucky.