~1~ The molecular weight of caffeine is 194, or ~200. So a 1 M concentration of caffeine is ~200 g/L.
~2~ Caffeine starts inhibiting DNA repair in cells at ~1 mM concentration in the surrounding fluid (blood, in our case). 1 mM = 1 M/1000 = 200 g/L/1000 = 200 mg/L.
~3~ The average cup of coffee contains 100 mg caffeine. Upon ingestion, this is diluted into your ~5 L of blood. Assuming 100% retention of the compound, caffeine's final concentration in your bloodstream is 100 mg/5 L = 20 mg/L. This is about ten times less than the active concentration of caffeine calculated in step 2.
So according to this back-of-the-envelope calculation, a single cup of coffee is unlikely to generate bloodstream caffeine concentrations that would inhibit DNA repair. Ten cups of coffee, however, might certainly be dangerous, and some energy drinks contain nearly this much. In addition, it is possible that daily consumption of caffeine has a cumulative effect.
Note: I am not a medical doctor, and this is not meant to be medical advice.