Jeepers, I just can't imagine anyone getting to Anadyr by road - there ain't any friggin' roads up there!
I regularly fly from Anadyr to Magadan (overnighting in both places) when I deliver turboprop aircraft, which is my day job. I've done that route about 5 times in the past year.
There are a few logging roads and a few trails in the Anadyr area, but once you get about 100 km southwest of Anadyr, you have reached the part of the world where the map says "here be dragons". There are very few settlements of any kind for the first 2/3 of the route to Magadan, and certainly no bridges over the rivers until you get quite close to Magadan. It's not unusual for me to fly for 150 km and see no evidence of human presence (now or previously) up in that area.
FWIW, if you are interested in riding in that part of the world, you might want to investigate riding in Alaska, perhaps travelling from Anchorage to Nome. Nome is not that far away from Anadyr, and it's basically the same kind of town as Anadyr - a remote settlement near the Bering Strait. The difference is that in Alaska, the people speak English, and relatively speaking, fewer permits would be involved.
As for Anadyr - normally, I overnight in Ugolny, which is the small village (about 2,000 people) beside the Anadyr Airport. Earlier this year, I thought it might be worthwhile to visit Anadyr itself, which requires a ferry ride (in summer) or helicopter trip (in winter) to reach from the airport.
Anadyr was not all that impressive. It was expensive. The tourist-oriented businesses there know that any tourist who visits will only pass through once, so they really put the screws to you so far as pricing is concerned. The old church is nice, but jeepers, for the price of getting to Anadyr to see it, you could go tour the most magnificent cathedrals of Europe.
As for any 'traditional way of life' - forget about it. Anadyr is a resource town, its economy (outside of the presence of government) is almost entirely based on supporting mineral exploration and mining development in the area.
Here's a photo I took this summer from the ferry - this shows the whole town