If you don't have much time to watch the Tour, you'll want to watch the stages with the greatest probability of being decisive to the race's outcome. Here they are.
Five High Mountain Stages
Stage 9 Sunday, July 13th
Stage 10 Monday, July 14th, uphill finish
Stage 15 Sunday, July 20th, uphill finish
Stage 16 Tuesday, July 22nd
Stage 17 Wednesday, July 23rd, uphill finish on L'Alpe d'Huez
The uphill finishes in the mountains are significant because often on descents riders will lose some of the advantage they gained by working hard on a climb. Riders will often attack aggressively on uphill finishes, it can change the outcome of the race and it's exhilarating to watch.
Two Time Trial Stages
Stage 4 Tuesday, July 8th
Stage 20 Saturday, July 26th