Translation:I will stay in the hotel and I will eat in the local restaurant.
In English it sounds awkward to repeat the subject in this way... "I will stay in the hotel and I will eat..". I think most English speakers would be more likely to say "I will stay in the hotel and eat in the local restaurant."
I'm wondering if there is also a tendency to do this in Irish, rather than repeating the subject after each verb? Would it be acceptable to say "Fanfaidh mé san óstán agus íosfaidh sa bhialann áitiúil"?
The subject generally gets repeated in Irish, but as you say, not in English -- at least not in U.S. English. The type of English translation you suggested should be accepted, i mo thuarimse féin.
I'd just advise doing that only with verbs that don't take a direct object. For example, you won't be able to say, "I'll stay here and eat the food" in that same way because it becomes, "Fanfaidh mé anseo agus íosfaidh an bia" which sounds like you're saying "The food will eat".
I keep getting these wrong for saying "at" instead if "in", it doesn't seem like an important distinction to me...