Okay I'm noticing a definite (and expected) trend here, no-one uses it, some would be interested in it for babysitting captured cities or new colonies.
What I've done is made it build basically in this order:
1: It builds culture to get the first border pop (sensibly, it only does for cre if the city is culturally pressured).
2: It builds a workboat if needed (this is generally the only unit it will build!) (will whip)
3: It builds growth emphasizing buildings - granary/lighthouse (will whip)
4: It builds a culture building if the city has no culture, unless the borders are already popped and there is no need for culture. (will whip, sometimes)
5: It'll build any old cheap building.
6: A happy build to cure unhappiness. (will whip)
7: A healthy build to cure unhealthiness. (will whip)
8: It builds a courthouse if at least 6 upkeep.
9: It builds a specialist-enabling building if it's running citizens.
10: It builds +exp buildings.
11: It builds any building.
12: It uses build research/wealth.
13: It gives up and trains a unit.
Note that the building order is the "guidelines" it uses. Where I've said "will whip" that means it WILL whip the build. The lack of will whip doesn't mean it wont whip it. It simply uses the AI whipping logic here which is fairly good if slightly on the gentle side.
It will NEVER choose a limited class building, meaning no wonders, no national wonders, no cathedrals. Of course you can still manually get the city to build anything you want.
Some comments:
5. Isn't it a good idea to build a Forge at his point? More hammers for the rest of the building queue...
13. I think it should NEVER build units (Research or Money is better). Specially settlers...