First: Don't use PRICELINE Name Your Own Price for 4 Stars in Universal Area, you are correct, you may get The Arnold Palmer's Bay Hill Club & Lodge.
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Instead, use PRICELINE EXPRESS Deal. Under Express Deal, find 4 star in Universal Studios Area. Check their price first.
Usually, for those 3 Loews on-site hotels, the Express Deal is around $220 or higher. No way it can be cheaper than $180, at least I never saw one. So if the 4 star Express Deal is in that price range, it should be one of the on-site hotel.
If the 4 star Express Deal is lower than $180, it could be end up The Arnold Palmer's Bay Hill Club & Lodge.
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Another factor is, if the 4 star Express Deal includes free parking, it's definitely NOT the on-site hotels. They don't offer free parking,
Another difference is, if 4 star Express Deal includes Pet-Friendly, it's definitely NOT the Arnold Palmer's Bay Hill Club & Lodge, because Arnold Palmer's Bay Hill Club & Lodge doesn't allow pet.
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Hopefully this helps. :)