Would has two possible meanings in this context:
- as the past of 'will', (something expected to happen) expressed from the viewpoint of the past
- to express a wish
going to expresses something already planned
I thought I would try eating Japanese food today.
As the past of "will", it means that I expected to eat Japanese food. Adding I thought indicates that the plan was frustrated: I did not, and probably will not eat Japanese food today. If not already mentioned, the speaker would normally go on to explain why the plan was frustrated.
As a wish, it means that, earlier today, I decided that it would be nice to eat Japanese food. If the speaker does not go on to describe the meal, the listener will assume that the person has not yet eaten Japanese food, but still has that wish- maybe will do later today. The listener might even regard it as an informal invitation to join the speaker for Japanese food.
I thought I was going to eat Japanese food today.
With something already planned, I thought implies that the plan was frustrated. This means that I decided earlier today, but my plan was frustrated and I have not yet, and probably will not.
With either frustrated plan, the speaker would emphasize the word thought.