Riyadh sucks. Absolutely positively nothing there that would appeal to a Western eye. And way too hot in the summer and surprisingly cold during winter.
Jeddah is actually pleasant! Not too warm in the summer (saw a max of 38C this summer) and hardly ever less than 20C in the winter. Jeddah, on the coast? Anything related to what we Westerners know as sea-side pleasures are ''Haram'' (NO-GO) for the Saudis.
However, you can buy access to several beach resorts, there are one to two diving enters around which are active over weekends. There is one public beach, and if bourkinis are your fetish, this is the place to go! No sailing, powerboat or jests, though (although I've seen the odd jets on the creek near the airport).
We are lodged on Falastine street near the fountain, thats a modern area with plenty of restaurants. The historic old town of Jeddah is a UnescoWorld Cultural Heritage Site, very impressive for eyes, nose and ears and I discover new details each time I wander around there. It is perfectly OK to walk around in shorts (well, avoid those really short ones, unless it's for jogging) and flip-flops.
I do my jogging on ''the Corniche'', thats the main sea-side walking promenade, and I meet at least one other jogger each time. This is to say that the place is not like Central Park, but still, the locals leave you in peace and don't cause problems. Had some locals in their dish-dashas run with me for a couple of minutes the other day, we were making selfies of each other and all by-standers were amused of the scene. No need for your wife to cover the hair or to mask her face. Only have her wear an Abaya. Found a lively shisha bar serving tasty fresh juices. Uber works well and is dead cheap. The Saudis, in contrary to what you may think, are quite laid-back and even fun-loving. They are helpful, polite and soft, in clear contradiction to their UAE and other Arab brothers. Exception being the immigration officers at the airport, who are more pre-occupied chatting on WhatsApp with their wives (plural) than serving the large queues of incoming travellers. One real good thing in the KSA is that you won't need to worry about pickpockets.
PM me for some tips for Jeddah restaurants, and, once here, I could take you to two places serving alcohol (unless you are Muslim yourself, or you tend to bring-in your own home distillery). First thing to do when you arrive here is to download a prayer App, 'cause the whole nation shuts down 6 times a day for 30 minutes during prayer. But you already knew that, I'm sure.
Red Sea Mall is the main shopping mall in Jeddah, if that's what you like, the supermarket there has good fish and tasty lamb chops.
Traffic can be dense here and both locals and Pakistani/Bengali expat drivers don't exhibit any discipline whatsoever while driving.