Airbnb or other apartment type accommodations are hands down the best option for travel with kids. Especially in Europe where the default is a room for 2 and you can’t have extra people in it. Of course you CAN find rooms for 3-4, but it’s pretty limiting. An apartment also gives more privacy (you have a bedroom(s) and a living room, making things like getting dressed easier). Finally, the ability to store food - cook or just snacks/picnic style stuff. In my experience this is especially helpful in Spain because at least my kids don’t love dinner at 10PM.
So…go with apartments
I always do, and have never had a doorman or anything. These cities are safe, especially in the main tourist areas. Those would be the easiest to stay in, closer to the sights and generally safe. There are safe areas outside the center, of course, but it’s less convenient and also might be harder to find out where is good.
I guess I’ve never worried about safety beyond double checking the locks and such at check-in. You can go to Google street view and look around the area. Perhaps ask the owner what floor the apartment is on and avoid ground floor, just in case? And if it’s very cheap compared to others of similar size in the area, that’s a flag to me. Not necessarily unsafe but…something makes it cheap and I don’t want to find out what!
Finally, if you are really concerned look for “serviced apartments” or “aparthotels”. These are often apartment style rooms with a bit more of a hotel set-up. I don’t know of any specifically in these cities but they might exist.