In the following, my textbook says that #1 is the correct choice.
(1) お食事の 際は、こちらのテーブルをお使いいただけます。
(2) ご飯を食べる 際は、こちらのテーブルをお使いいただけます。
I think that both are grammatically correct and have the same meaning (ignoring whatever "nuance"). What am I missing?
And what about this? Is it grammatically correct? Does it sound natural?
(3) お食事する際は、こちらのテーブルをお使いいただけます。
This looks primarily like a 敬語{けいご} problem, more than a syntax or semantics problem.
お使いいただく is 敬語, and 食べる does not match it at all. 食べる is neither 尊敬語 nor 謙譲語. This means that 「ご飯を食べる」 is not even polite when 私 is the one doing the eating.
There are many ways to say (あなたが)食べる in 敬語:
(私が)食べる in 敬語:
Your example #3 has a problem with the する:
(あなたが)する in 敬語
(私が)する in 敬語
Minor technicality: 食事 as a noun is a little tricky because it could change depending on who provided the meal. 「お食事」 will work in both 私が and あなたが contexts, except for when you are the one eating a meal that is not provided by someone who should be shown respect. Like if you are eating a meal provided by yourself, that would be 「食事」 and not 「お食事」.
So, with that in mind, there are many possible combinations depending on who is doing what:
The point is that sentence #2 in your textbook is wrong in any possible situation, because 「食べる」 is inappropriate in a 敬語 context.
(*1) An instance of redundant keigo (二重敬語) that is technically incorrect, but has taken root by custom (文化庁『敬語の指針』 p.30).
Since 際 is a noun, all three sentences are more or less valid regarding basic grammar. But grammar and usage are two different things, while something may be grammatical it could sound unnatural and so is ご飯を食べる際.
際 is used in special occasions in place of 時 and special occassions tend to like sino-japanese vocabulary rather than vernacular vocabulary, hence the choice of 食事. Of course, a special occasion can be described without sino-japanese coumpounds but "to eat a meal" is not really something special unless if done in a peculiar setting.
An example of special occasion could be, 二人きりで散歩した際にようやく告白ができた。 Here 時 would have been possible to use but the use of 際 make the situation more "unique" to your eyes.
(1) and (2) are grammaticaly fine, and (3) needs a little fix if you want to keep お before 食事 (お食事をする際に…) (but since a する-verb is also a noun you can just drop the をする and instead put の which leads to (1)).
As you say, both (1) and (2) are grammatically fine. However, (2) is disproportional in the point that it adopts a humble verb in the main clause while the former clause doesn't use some respectful expression.
The problem of (3) is, you use a humble verb for the action of the listeners. If the location is one that should be respected, that would be a valid expression. Or it could be accepted as a euphemism (so called 謙譲語２) But that's not likely the case, considering that you use a humble verb いただけます to the listeners.
(Please see this post as an appendix to @mirka's answer.)
(1) お食事の際は、こちらのテーブルをお使いいただけます。
こちらのテーブルをお使いいただけます is polite and formal, using こちら (= more formal than こっち) and (お～)いただく (= the humble form of (～して)もらう), so polite/formal お食事の際は is appropriate here.
(2) ご飯を食べる際は、こちらのテーブルをお使いいただけます。
This sounds awkward (though is not grammatically/semantically wrong), because ご飯を食べる is casual while 際 and こちらのテーブルをお使いいただけます sound formal. With ご飯を食べる, you'd say more like:
(2') ご飯を食べる時は、こっちのテーブルを使っていいよ。/ 使ってもらっていいよ。etc.
which would sound quite casual. You might say it to your family or friends, but not to your boss or customers.
(3) お食事する際は、こちらのテーブルをお使いいただけます。
You'd change お食事する to the honorific form, as in @mirka's post. (And it would also help to clearly show that the subject for 食事する is the listener.)
(3') お食事をされる際は、こちらのテーブルをお使いいただけます。
or
(3") お食事される際は、こちらのテーブルをお使いいただけます。
Hope this helps.
