Most suitable area to live in Kuwait for European couple?

Hello Sarah and welcome to the forum. Pretty much the only place that fits your description, especially the part about being "walk friendly" is Salmiya. Salmiya is a popular neighbourhood pecisely for this reason, but I avoid it as my office in not close and it is crowded. That being said, Salmiya mostly consists of multistorey residential buildings, which may be a problem if you are looking to bring your dog over. In that case an apartment or a floor in a villa or a smaller building with a yard might be more suitable, but you won't find those in Salmiya. Salwa though is close by and you could find something there that might be more suitable.

Sometimes landlords specifically tell if the pets are allowed or not, but it is best to check. Culturally cats are more tolerated than dogs.

We have used Pet Land (http://www.petlandkw.com) for our two cats and it worked out fine.

Let me know if you got any specific questions.

Its better rent a house or apartment near your work location