Most tourists who land at Queen Alia's airport Amman they leave the capital as soon as possible for other destinations. I used the Royal Jordanian from Barcelona, ​​but it runs the same route (only from March, though). To enter in Jordan the visa which can be purchased at the airport and costs 40 dinars (JD).
Recent political events in this part of the world make many think that Jordan is not a safe country; in reality it is not so, it is not at war with anyone and the frequent police checks serve to reassure, rather than the opposite!
Amman is a very large and chaotic city which it extends over seven hills and spreads out towards the wide and still empty surroundings. Cars seem to outweigh pedestrians, public transport is scarce, there are taxis everywhere and taxi drivers who are not particularly friendly. But I recommend you visit it, because it is a city with a long history and great contrasts where you will happen to see a flock of sheep grazing on a meadow between two embassies, in a fairly chic neighborhood. The history of this city can be traced back to its most famous monuments. I first visited the Citadel, which is located on the Jabal al-Qala'a hill; first Ammonite acropolis, then Roman, then Byzantine, the citadel for a 1 JD ticket (the local currency, practically equal to just over 1 euro) will allow you to enjoy the archaeological area and a amazing view on the metropolis.
The most beautiful monuments are the temple of Hercules (built at the time of Marcus Aurelius) with majestic columns, the Palazzo del throne, the Byzantine basilica. There is also a museum that displays artifacts from various civilizations, from the Neolithic to the Ottomans.
From the Citadel a steep descent on foot leads to the remains of the grandiose anfiteatro Roman, that Antonino Pio had built close to the hill. It is huge - 6000 spectators - with very steep steps and admission costs 1 JD. From those steps the noise of the cars in circulation seems completely unnatural. From the amphitheater on foot you can reach the suk, the soul of downtown. This is a grand bazaar where you can buy everything. The narrow streets that lead inside are monothematic, with shops selling the same items, from gold to spices, from underwear to furniture. There is also a large food market, with beautiful Jordanian fruit and vegetables - the mild climate allows for uninterrupted production of tomatoes, cucumbers, peppers, aubergines which are omnipresent in the local cuisine. Do not miss the shops of spices and aromatic plants or herbs, with giant sacks that sell cinnamon, pepper, oregano, turmeric, chilli and a thousand other unknown varieties but all to try. Spices are also an ideal gift for a friend or grandmother: they weigh very little, do not clutter and are certainly 100% typical!
souk of Amman
Speaking eat: downtown there are several shops or clubs that do delicious falafel, served in the bread here, “Falafel” is the magic word for a roll of Arab bread stuffed with a freshly made chickpea meatball, with tahini sauce and some tomatoes; from Hashem with 1 JD we eat and drink. I have also experienced the delicious knafah, a dessert of fresh cheese, pasta, honey and chopped pistachios that is served hot: it exists in two versions, more crunchy or softer but I can assure you that it is irresistible (as well as an absolute calorie bomb).
If, on the other hand, it is thirst that you have to defeat, forget the beer: alcohol is off limits in any public place. Instead, there are fresh fruit juices - try the pomegranate - on every corner and a delicious Lemun ma nana drink (lemonade with mint and ice) absolutely thirst-quenching.
Il suk it is a great cauldron of perfumes - sometimes smells - colors, screams and confusion, it is the soul of the most popular city and probably similar to the souks of other North African or Middle Eastern cities.
But Amman has many faces and it is enough to climb one of its hills to discover completely different streets and shops.
Right above the amphitheater is al-Rainbow street, a street that I recommend not to miss for the beautiful international atmosphere that reigns there. Here the chaotic downtown traffic is not there and shopping opportunities are not lacking. Some of Jordan's most interesting private foundations have their own boutiques around here. For example. there Jordan River Foundation which promotes quality craftsmanship and guarantees a salary to women who work and where you can find beautiful objects for the home (pottery, pillows, tapestries, but also dolls, T-shirts and small jewelry). The one in the photo is the small garden in front of the shop.
Another beautiful Jordanian institution is the Royal Society, which manages alternative tourism routes, promoting Bedouin trekking and traditions; here in Rainbow-street they have the Wild Jordan Café, a super panoramic place in Amman where you can eat organic food or drink a tea or coffee produced by their associates. Next to the restaurant is the shop, with a lot of handicrafts for all budgets and personal hygiene products made with natural raw materials (soaps, essences, herbal teas).
Walking down al-Rainbow street you can make a small digression and look for the alley of the Soap House, a company that produces soap, body creams, personal hygiene products with a thousand scents and in very elegant packaging. Even if the boutique is very elegant, the prices are achievable, especially when compared to the cosmetics of large companies.
If you are looking for books, Middle Eastern or Arabic authors or simply a book in English, you should not miss it Books @ Café: a delightful library full of titles. Upstairs is a somewhat noisy café-restaurant.
Another little place that I can recommend a few meters from the library is the Art Gallery Jacaranda: not exactly low cost. Even if it is an art gallery, you can find stationery items - diaries, postcards, notebooks - very special and at affordable prices, useful for making a gift. The engravings and prints are very interesting, but not the best of comfort to be transported by plane.
Leaving al-Rainbow street and its surroundings, but remaining in the more elegant Amman, the visit to the center Darat al Funun www.daratalfunun.org will amaze you. It is a center dedicated to art consisting of some houses in the local architecture, surrounded by a splendid garden, which cyclically host contemporary art exhibitions. In the garden there is also a pleasant outdoor café, where you can linger while sipping Turkish coffee or the inevitable, delicious mint tea.
Are you looking for a hotel? Amman has many modern districts, with all the major luxury hotel chains in the West; but a nice and inexpensive accommodation is the Bonita Inn, on the third circle. The 6 rooms are clean and comfortable, the restaurant does Spanish cuisine (and well!). Downtown instead is the Art Hotel, managed - among others - by an Italian: well-furnished rooms, with breakfast. It is advisable to ask for a room not facing the busy main road.
Well, the dinner advice is missing. What do you eat here? Many appetizers, hot and cold, terrines, meat dishes, vegetables prepared in a thousand ways, a paradise for vegetarians like me. Amman is not expensive, precisely because it is not very touristy.
There is no shortage of restaurants: you can recognize the slightly more cosmopolitan clubs for non-Arab patrons. You can choose Italian Lorca (well, someone will have to tell them that Federico Garcia was not Italian) with a nice atmosphere and low prices, in Albaouneya Street; or play it safe with Suffers, coincidentally in al-Rainbow street. The public is not only cosmopolitan but also local; very well-kept environment, panoramic terrace, wide range of Jordanian and Lebanese food, open all day even just for tea or cake. If you want, they also bring you shisha for smoking. An employee ceaselessly produces Arab bread, introduces it into an oven located in a corner of the room with skillful maneuvers and takes it out of the oven after a few minutes: they will bring it, warm and irresistible, in a basket. 
For a big dinner the bill was 15JD, you can stay there, right?
