You mentioned half a day trip to Kamakura so I am assuming that you want to be back at Tokyo around 12 noon – 1 p.m.

There is a direct train from Tokyo station to Kamakura station, the train ride is about 55 minutes from Tokyo station to Kamakura station, fare is JYP 890. There is a train depart Tokyo station at 7:12 a.m. and arrive at Kamakura station 8:07 a.m. Little caution, trains to Kamakura depart from underground platform at Tokyo station which takes little time to get there from the ground level. I will be at Tokyo station more than 10 minutes before departure to make sure.

I will list two top tourist sights in Kamakura: Kamakura Daibutsu (Great Buddha, 鎌倉大仏) which is located at a temple called Kotokuinn (高徳院), another is Tsuruoka Hachimann Guu (Hachimann shrine or Tsuruoka shrine,　鶴岡八幡宮).

The temple for Great Buddha opens for public at 8 a.m. It is 10 minute bus ride from Kamakura station, or you transfer to another train at Kamakura station, Enoden, and get off at third station from Kamakura station, Hase station (about 7 minutes ride). Then 7 minutes walk from Hase station to Great Buddha. Realistically speaking you want to see 20 minutes plus to get from Kamakura station to Great Buddha, because you can easily wait 5-10 minutes for next bus or train.

Tsuruoka shrine is 10 minutes walk from Kamakura station, which opens for public at 8:30 a.m. I think getting from Great Buddha to Tsuruoka shrine can take around 30 munities or more.

May be you start to get the picture. You will not have a lot of time to see each places and soon it will be 11 a.m., time to head back to Tokyo.

Also, if you are wake from early morning to see the fish market at Tsukiji, then it is also likely that you may start to feel tired and sleepy before 12 noon. I think something to think about…