Nikko or Kamakura?

Hello! I could finally book my trip to Japan next October and I am really looking forward to it. I will be arriving early in the morning in Osaka and spend one night there; then 4 nights in Kyoto (with side trips to Nara and Himeji castle) and finally 4 nights in Tokyo with my flight back to Europe late in the 5th night.
I think I am just a little tight in Tokyo and I think I will have time for only one daytrip. Should I go to Nikko or Kamakura? I am aware that Nikko is described by many as more beautiful than Kamakura but also that it is much farther from Tokyo. Moreover I read major reconstraction works are in progress in some of the main toutist sites there and I am afraid thay could ruin a visit there. Considering all that, what is therefore the best daytrip from Tokyo? Is a visit to Kamakura doable in half a day?
Thank you for your kind help.

Nikko is fantastic even with buildings covered for reconstruction. However if you have seen lots of temples in Kyoto then nIkko or Kamakura are more of the same. I would consider doing a day trip to Hakone and seeing Mt Fuji and the Open Air Art Museum.

If you go to Kamakura you would miss out if you did a half day, Hire a bicycle and ride around the various temples.