Where to stay
Amman offers a lot of accommodation options for almost every range you are looking at. Websites such as Booking.com and Airbnb are available and should provide you with a wide number of hotel and apartment options to choose from.
But here are some possibilities to help you get started:
Chain hotels:
Jordan InterContinental Hotel, Grand Hyatt Amman W Amman, Sheraton Amman Al Nabil Hotel, Amman Marriott Hotel. We'd say almost every hotel chain you know is present in Amman. So please give it ago and search for any name you may have a preference for.
Botiques: AlQasr Metropole Hotel, The Conroy, Bonita Inn, La Locanda, The House Botique Suites, Hisham Hotel
Airbnb: Amman can be bigger than what you think. If you choose to stay at an apartment, please make sure (by using google maps) that the address is not more than a 10 mins drive to/from the 4th circle.
There are several chain hotels in Aqaba. We highly recommend that you book a hotel with a beach access.
Two popular areas are Ayla and Tala Bay. Ayla is really up and coming and we hear great things about it from people who've been recently.
Outside of both Ayla and Tala Bay, the Kempinski is a good recommendation. It is close by from Ayla so you can stay there and spend time in Ayla for lunches/ dinners.
Booking.com and Airbnb work here as well but we'd recommend either the Movenpick Resort Petra or Petra Marriott Hotel. Both are great options with the Movenpick being very close to the historic site while the Marriot sits on top of a hill offering a great view onto a rosy mountain range!
You think fancy and desert wouldn't go together? Think twice. There are a number of great "camps"/ hotels in the middle of the desert offering a great chance to soak on the surrounding while having all your relaxation wishes taken care of. No matter which one you choose, we highly recommend that you go for a "bubble". And we mean a bubble hotel :)