What time should a 10 year old go to bed?

It depends on what time they need to be up at.

No later than 10:30 on a school night. If they have to go to bed at 7:30, 9:00 or 9:30 would work. Or, perhaps, by 9:00 they have to be in bed and they can read quietly until 9:15 or 9:30.

On weekends, 11:30 should be max (with midnight for special occasions); but the time before can be allotted whether the child has behaved, etc. and is based on the parents' discretion.