One single nuke plant built since 2000....2016, Watt’s Bar #2 in Tenn. After that, it was 1996 when another plant was built (Watt’s Bar #1). The TVA folks are about the only ones with any ‘gut’ to go and do this.
Nuclear power plant construction costs around $8,000 per kwh these days, not including the huge future deconstruction costs. Solar is around $3,000 and natural gas combined cycle is about $614. Because of horizontal fracking technology there's a huge supply natural gas in the USA these days. Sometimes producers will pay to have it taken off their hands.
Construction of the Watts Bar nuclear plant began back in 1973.