Hi there...
I was in Nome one year ago today, and we had 2.4 inches of snow! It was not the nicest weather for walking around

There's really not a whole lot to walk around and see. I did spend about an hour at the McLain museum, which was rather interesting. The National Park Service has a small visitor center (on Front Street) for the Bering Land Bridge National Preserve. There are a couple decent gift shops. As for gold mines, there will likely be some folks on the beach using some heavy duty equipment to look for gold, but I don't recall any mines open to the public (but that may just be my memory).

I tend to be somebody who likes to drive to the end of the road, so that was more my goal last year.

You could check with the visitor center to see if they know of any place that rents bikes or maybe even an ATV. See http://www.nomealaska.org/vc/ There are only two places that rent vehicles, and IIRC,those are about $110 per day, as of last year.

riftime