Tsunoshima lighthouse or Kintaikyo bridge

I have made Okayama my base city for the 2nd leg of my trip before I end off in Fukuoka/Hakata city on the 7th day of my JR pass and will take 1 day to Yamaguchi. 1) Which is better to visit, Tsunoshima lighthouse/Bridge or Kintaikyo bridge? I understand these 2 areas are not near each other. I am travelling with my parents, husband and 2 kids aged 5 and 10 years old. We have bought the JR Sanyo Sanin pass and will not be driving, hence mode of transportation will be Shinkasen, local trains and buses.
2) For another day trip, which is better, Takamatsu or Wakayama? My other day trips will be Tottori and Himeji. Thank you.

Tsunoshima lighthouse/Bridge or Kintaikyo bridge?

If I were to choose, I would not hesitate to select Kintaikyo bridge.

More than just a bridge.
There is a beautiful park as well as the castle after the Kintaikyo bridge!

"Which is better to visit, Tsunoshima lighthouse/Bridge or Kintaikyo bridge?"

Given that you're relying on public transport, Iwakuni - for Kintai-kyō - might be a better choice as it seems to be more easily accessible. Tsunoshima would require a long northwards detour up from Shimonoseki, whereas Iwakuni is "along the way" (so to speak) between Okayama and Fukuoka. Also, as mentioned in the earlier comments, there's quite a bit more to see in the city than just the bridge.

https://ittekuru.com/2017/04/16/field-report-iwakuni-japan-16-november...

"For another day trip, which is better, Takamatsu or Wakayama?"

I'd go with Takamatsu. Easy side trip out of Okayama, nice castle ruins, splendid traditional garden, and a good place to try a local speciality (Sanuki udon).

https://ittekuru.com/tag/takamatsu/

I rather liked Wakayama Castle, but it's a rather long double-back from your Okayama base.

https://ittekuru.com/2014/07/28/field-report-wakayama-11-february-2014...

Cheers.

Beyond Kintai-kyo the area has something like 21 different attractions/spots that provide varying levels of interest/things to do. The local area website has a lot of information, but in Japanese.
I have seen some pretty inaccurate reviews of the area, but often visit. I've never bothered visiting the castle as I usually combine my visits with Miyajima.