How do I set start date with the core date field? I need set the start date (e.g. now +1) for my date field. How can I do this on Drupal 8.1.x?
When you create your field, you have the option of setting a default value.  Set the Default Value to Relative Date and then ender "+1 day" into the textfield, and proceed with setting up the field.

When you create new entities with that field, it will default to the current time +1 day, which you can then change if needed.