I've been searching all over the web for statistics from bike races, starting with the Tour de France because it is the largest. Stats I have been able to find include each stage's winner with their time. I'm just wondering if anyone knows a good resource for pro cycling stats like time per km or per segment within the stage. I'm pretty curious about the riders performance at certain parts of the stages.
Depending on what you're looking for, a site like trainingpeaks.com might meet your needs. You can often find power meter data files for riders collected during both the Grand Tours (the Tour de France, the Giro d'Italia, and the Vuelta a Espana) as well as many one-day classics (like the Ronde van Vlaanderen (the Tour of Flanders) or Paris-Roubaix). From these data you can extract speed, power, cadence, gear ratios, pedal force, heart rate, and slope over different segments of a race. In certain circumstances you can estimate aerodynamic drag and other parameters of performance.
This is pretty easy to answer. Several professional cyclists do already record their rides on Strava. A couple of the current most well-known male cyclists riding at UCI-level are Laurens Ten Dam and Taylor Phinney. You can see a full list covering various disciplines, levels and both genders at http://www.strava.com/pros .
This is about as close as you'll get to tracking actual athletes' times on specific segments of a race route. However, if you expect to find this data for all pros then your expectations are unrealistic.
Incidentally if you're interested in race stats you've hopefully already encountered the incredibly comprehensive http://www.procyclingstats.com .