First there's Nizhny Novgorod (host city) and just Novgorod. Sometimes called Stary (old) Novgorod. Very different places. Nizhny is a giant boring industrial city. Novgorod is a medieval city well suited to accommodate visitors. It's near St Petersburg. Maybe an hour away I can't remember exactly. Vladimir and Suzdal can be done on day trips form Moscow as Novgorod can be done from St Petersburg. The reason to go to appreciate rural Russia in a place that actually has tourist infrastructure and it's the foundation of the Russian state. Thousand year old churches and Kremlins etc. The above is like the base Russia itinerary for any first time visitor. The Solovetsky islands aren't too far if you fly. Irkutsk is far but I guess it's up to you if you want to make the trek. Nalchik is not close to Sochi. With a helicopter it's close but by train or bus it takes forever. The reason to go is the natural setting and unique culture. Again that's up to you if it's something you're into. If you only want to visit host cities I'd probably only suggest Kazan Moscow and St. Petersburg as worth the effort on the city alone.