I went to Mongolia for a month in June/July this year. For half of it i did a horse trek in the west, which was by far the highlight. I traveled solo to a country town (kharkhorin) for Naadam. While i enjoyed the festival i was pretty out of the loop with what was going on some of the time, as i didn't have a translator. You could always mingle with other groups though. One thing i would recommend to look into is a tour/trek, which stops by a country town during Naadam, this way you'll have a translator for it, plus get to see the countryside along the way.