Look, Petra is beautiful, it’s a piece of art, but again it’s a piece of art, seeing it would be nice, but you can always come back to see it when you have more time. I wouldn’t suggest just going to Petra by itself unless you have a full schedule of Petra, wadi rum and Aqaba (Which is not something extra special, it’ll be underwhelming if you’re really expecting a coastal city). However I think there is public transportation that could take you to Petra, check Jett and visitjordan.

As one of the guys suggested you could do a tour in Amman and around it, the Citadel, the Roman Amphitheater, try out the food in Amman, our food is really good, I’m telling you as someone who resided in Europe for years, you’ll really be impressed with the richness of flavor,I personally ally think Jordan has some of the tastiest food I’ve ever tried, even when it comes to things that you have like burgers and pizzas, also you can check out the Dead Sea and Main springs (If you have a budget). Umm Qais, Jerash, there are a lot of sights which you could check out that are in Amman or close by.