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.