For several years I've been making occasional short trips to Moscow for business or pleasure. As you can imagine, by now I've visited an awful lot of Russian museums, churches, galleries, restaurants, and cultural events. But my favourite outing so far was to VDNKh, a huge Soviet-era exhibition grounds with pavilions dedicated to (and often still hosting events, stores, markets, and eateries by) that country's national groups: Turkmens, Uzbeks, Belarusians, Karelians, Armenians, etc.
Like the USSR, Russia is a multi-ethnic country, and I'd love to see some parts of it that aren't overwhelmingly ethnically Russian. The problem is that I usually fly in or out of Moscow, and have only one or two days available for sightseeing.
What day trips or overnight trips can I take from Moscow to touristically interesting cities or regions representing Russia's non-Russian ethnicities? For example, are there fast trains or buses to Mordovia, Mari El, or Chuvashia, and if so, are there any cultural events or exhibitions there worth seeing? Or are there perhaps any smaller non-Russian towns to visit in the oblasts surrounding Moscow?