The awesome power of exponential tipping points is not to be underestimated. When the cost/kWh curves intersect, it could happen fast. Look at the adoption of the Internet and smart phones for examples. Solar could go from <1% of our energy to >25% in 5-10 years. That might be conservative.
I'm seeing nuclear as a niche technology. In a post-fossil world I can see it for radionucleotide production (e.g. for nuclear medicine and space probes), maybe for a few really heavy industrial needs, and for some locations with very poor local renewable energy availability. But for the most part I see it as obsolescent.
I do think it might find its killer app somewhere else though: Mars. There are many reasons it would make more sense there.