1) We'll wait until a table becomes available.
「テーブルが空くまで待ちます。」
「テーブルが空くまで」は until a table becomes available
2) We'll wait for some empty seats.
「席が空くまで待ちます。」
直訳すると「空の席のために待ちます」となり「席が空くまで待つ」という意味になります。
ご参考になれば幸いです！
When there is a wait for a table at a restaurant, usually the hostess at the front will let you know about how long she expects the wait to be. Then you will have the choice to wait or not. If there is nobody waiting ahead of you, you could say "I'll wait for the next available table." or if there are others waiting you could say "We'll wait until a table is available." Usually at busy restaurants there is a list of people waiting in order that they arrived so you could also say, "Please put us on the list for a table." This is standard procedure in the US, so the hostess will then call your name when your table is ready.
レストランでテーブルが空いていないときには、たいてい女性スタッフが入り口で待ち時間がどれくらいなのかを教えてくれます。それを受けて、待つかどうかを決めます。もし自分の前に待っている人が誰もいないなら、"I'll wait for the next available table."（次にテーブルが空くのを待ちます）と言えます。
もし他に待っている人がいるなら、"We'll wait until a table is available."（テーブルが空くのを待ちます）と言えます。
繁盛しているレストランではたいてい、客が着いた順に名前を書いていく順番待ちリストがあります。
ですから、"Please put us on the list for a table."（テーブルのリストに名前を載せておいてください）と言うこともできます。これはアメリカでは一般的な手法で、テーブルが空くとスタッフが名前を呼んでくれます。
"I would really like to eat here, so I am ok with waiting until a table is free"
"We have no problem waiting until a table becomes free"
If you went to a restaurant but they are full and do not have any tables free, but want to let them know you are willing to wait, you could say any of the following: "I'll/We'll wait until a table opens", "I would really like to eat here, so I am ok with waiting until a table is free" or "We have no problem waiting until a table becomes free".
レストランに行ったけれど、満席で相手いる席がないけれど待ちたいことを伝えるフレーズです。
"I'll/We'll wait until a table opens"
（席が空くまで待ちます。）
"I would really like to eat here, so I am ok with waiting until a table is free"
（すごくここで食べたいので、席が空くまで待っても大丈夫だよ。）
"We have no problem waiting until a table becomes free"
（席が空くまで待っていても大丈夫だよ。）
We do not have a problem with waiting for a table to open up.
We would be happy to wait for seats to become available.
We do not mind waiting for a table.
Native Speakers often say "~do not mind". It means that you have no problem with it and it does not bother you.
So by saying this, you are simply telling the person that you are not bothered by having to wait to be escorted to an available table.
We do not have a problem with waiting for a table to open up.
This means that you are fine with waiting for a party to finish and to accept their open seats. You have no problem with sitting in the waiting area until there is a vacancy of seats.
If something is vacant, it is open or empty.
We would be happy to wait for seats to become available.
The same as the previous answers, you are stating that it would not be a bother for you to wait. You are saying that you would be happy if you need to wait for a table to become available, because you really want to eat there.
We do not mind waiting for a table.
（席が空くまで待ちたいです。）
ネイティブスピーカーはよく "~do not mind"と言います。これは、問題ないこと、気にならないということを意味します。こう言うことで、相手に席が空くまで待つことが問題ないことを伝えることができます。
We do not have a problem with waiting for a table to open up.
（席が空くまで待つのは構いません。）
これは、席が空くまで待っていてもいいことを意味します。席が空くまで、待つエリアで座って待っていても構わないということです。 vacantは、空いている、空席のという意味です。
We would be happy to wait for seats to become available.
（席が空くまで待っていても構いません。）
これは、上の例と同じで、待つのが嫌ではないという意味です。そこですごく食事をしたいので、席があくまで待っていても構わないということを表しています。
When talking about a table being empty after people have been sitting there this is called to 'become available' or to 'become free'
'we will wait' or 'we don;t mind waiting' tells them you will wait for a table to become free
誰かが使っていた席が空くことは、'become available' や 'become free' で表せます。
'we will wait' または 'we don't mind waiting' で、「席が空くまで待つ」と伝えられます。
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