Expressing “to” - stuff to do, a movie to see, etc

Question

how would this use of “to” be expressed in japanese?

There are three new movies to see at the theater!

We have more food to eat.

Answer 1

You can use ～べき when this "to ～" means "which one should/must ～". This is unambiguous but relatively stiff.

• やるべき作業がまだある。
  There are still tasks to do.
• 読むべき教科書を教えて下さい。
  Please tell me the textbook to read.
• あれは絶対に見るべき映画です！
  That's definitely a movie to watch!

You can say やらないといけない作業, 読む必要がある教科書, 見た方がいい映画 and so on, too.

You can also use plain relative clauses like やる作業 as long as they do not introduce ambiguity. But you have to be careful because relative clauses have various usages. やる作業 usually means "tasks to do", but 飲むヨーグルト means "drinkable/liquid yogurt" rather than "yogurt you must drink", and 見る人 usually means "observer" rather than "person you should see".

And there are quite a few stem + もの words which roughly mean thing to (verb) on its own. 食べ物 literally means "things to eat" already. To translate "food to eat", 食べる(べき)食べ物 sounds very redundant. Simple 食べ物 should be fine in most cases, but you can also say 食べるもの ("things to eat") if you want to emphasize the nuance of "to eat" or "must/can eat".