There should be no issues with having many Apple Tvs close to each other.
The issue is most things on the Apple Tv, require an account to use and watch content.
Is the hotel planning on setting up the Apple TVs with their own account and just letting guests buy or rent anything they want?
What about other channels or apps, like Netflix, Hulu etc... those also require a subscription. Will the Hotel provide this subscription?
How would you keep track of what purchases or rentals are made by what room to charge for them if you are planning on charging them?
What exactly is the end goal here, by having Apple TVs?