Gonna repost Rollercoaster Tycoon (any), Tropico, Black and White, Anno series (1602), and Zoo Tycoon, and the Sims
I underlined the ones that are the easiest and offer no "threat" to the player. Tropico, you can get voted out and have military coups form. Black and white involves simplistic battles against other Gods, Anno get more complex and/or smarter AI as the game series goes on. 1602 A.D. (US release title) was the first in the series. The AI never makes an assault. You could theoretically take over the whole map with 1 cannon and about 2 large warships if you know how to exploit the AI. (In a way, I have done it before.)
Both of these Tycoon games are relatively high budget and I have yet to find a kid that doesn't like them. It is very easy to make money just by putting in attractions. YOu have to watch out for low budget crap Tycoon games in the series. Some of them look like they are coded by high school kids and had a budget of 500 dollars. Some Tycoon series games are no more than shovelware. These two titles, and Railroad Tycoon got a decent enough budget. However, Railroad Tycoon has some complexity to its economic system.