Jordan - make sure you also go to Little Petra, go right to the end, there’s a narrow pathway that takes you to an amazing plateau with great views (and if you’re lucky you’ll be “rescued “ by a gorgeous Jordanian soldier).
Istanbul is fabulous, don’t miss the Cistern, catch the public boat up the Bosporus to Rumeli Castle. Easily 5 days of exploring, you could even take a day trip by bus to Edirne.
Granada, also beautiful loads to see, make sure you stay in the old city and see a flamenco show, a bit touristy, but still fantastic. The high speed trains also mean that you can easily do a day trip to Córdoba.
Beirut - fabulous, just don’t think of driving.
Chicago was brilliant, we went in May this year, the tourism office in Macy’s is lovely, I don’t think they get many visitors (everyone does their research online) they were super helpful. We did an amazing river tour run by the Architectural Society. The Art Institute is unbelievable. The old Public Library is now a free exhibition centre, it has a Tiffany glass dome and amazing Tiffany mosaics everywhere, like being in a jewel box.
Canterbury is great, but I’m biased as I went to University there.
If you can handle long haul, Bangkok is my favourite city, just so much to do, but the jet lag may be a bit much for 5 days.