Ci vediamo domani basically means "see you tomorrow" http://www.wordreference.com/enit/see%20you%20tomorrow
"Let's see each other tomorrow in the gym" shouldn't this also be accepted ?
would we be penalised if we made the sentence future tense - we will see each other at the gym tomorrow?
No, we wouldn't be penalized if we translated this sentence into future tense especially when there is an element referring to near future "domani". I would just slightly alter the word order to match that of the Italian sentence : "We will see each other tomorrow at the gym."
The present tense is often used to express what will happen in the future. If another element in the sentence refers to the future, the present tense can be used. http://italian.about.com/od/verbs/a/italian-verbs-present-tense.htm
I put We'll see you tomorrow in the gym and it was rejected. Nov 2018.
It is an idiom that translates as "See you tomorrow" and is not reflexive in English. In German we say "Wir sehen uns morgen" and some Germans mistakenly say "we see us tomorrow". Translating it as "we see each other" might be closer in meaning but sounds awkward.