Priority and advantages (or benefits) at our services and facilities

I think you need to be careful about using the word "amenities" here, as this often refers to the complementary toiletries and/or gifts in the hotel room itself.

This may work?

[Enjoy] preferential services and amenities at our establishments/hotels

grand premium room garden view
www.calypso.net.au/r/agweb/gogo-gw/agweb/print/GW/H/MBJ/LBR...
THE LEVEL Oceanfront accommodations are located in an exclusive area of the resort and feature **preferential services and amenities**, a private check-in/out ...

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Note added at 3 hrs (2016-07-08 20:50:39 GMT)
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https://uk.answers.yahoo.com/question/index?qid=201106150631...
What does amenities mean in terms in components of tourism?
Best Answer: Amenities are any tangible or intangible benefits of a property, especially those that increase its attractiveness or value or that contribute to its comfort or convenience.
Tangible amenities might include attractive guest rooms (lodging), dining, parks, swimming pools, health club facilities, party rooms, theater or media rooms, bike paths, community centers, services, or garages, for example.
Intangible amenities might include pleasant views, nearby activities, good schools (in the case of residential real estate), or a low crime rate, all of which add to the desirability of a property.