You lose 3 production (2 from palace and 1 from city tile) for every turn you move
So the three production mentioned plus the tile you would have been working is the loss per turn... normally 1-2 prod. So lets just assume 5 production.
A common reason to move is to the top of a plains hill. You will loose 5 prod for each turn to get there but will gain an extra prod on getting there so can quickly make up for it. Moving one turn to a plains hill means you gain an extra production after 5 turns but did loose prod initially. It really is a common thing to do. Two turns can be riskier on higher levels and 3 turns I start to doubt.
Moving to a grassland hill gives no benefit beyond defense, its not something I will do typically.
Moving on to a luxury if it takes half a turn I will always consider. The extra trade it will give and 5% initially until trade is worth consideration but especially if it gives science or culture it is a significant benefit in the early stages.
Having cows immediately screams Great Zimbabwe and so moving to get more resources is an option. One problem is you do not have 3 tile visibility when you start so there is always some unknown in there.
Cows,sheep,horses - God of the open sky - that cultural bump early is beyond good.
Horses rush for horesmen is always tempting. If nothing else they sell well.
Plantations? Oral tradition.... get those bananas within the first 2 rings
Moving far has its risks, especially when you are unknowingly moving towards another civ. I tend not to move far and this makes sense as you realistically should be only moving toward something you can see (revealed by warrior moving first)
If settling on a featureless grassland with nowhere else better in sight you may be better if determined not to restart, of just settling on turn 1 where you are. You still get 3 production worst case for your capital.
