Basic script for Blender Python nodes

nodetest.py

import bpy
from bpy.props import IntProperty, FloatProperty, PointerProperty
import nodeitems_utils
from nodeitems_utils import NodeItem, NodeCategory

bl_info = {
  "name": "Custom nodes",
  "category": "Node",
}

class CustomPropertyGroup(bpy.types.PropertyGroup):
  int_value = IntProperty()
  float_value = FloatProperty()
  
  def draw(self, context, layout):
    row = layout.row()
    row.prop(self, "int_value")
    row = layout.row()
    row.prop(self, "float_value")

class CustomPanel(bpy.types.Panel):
  bl_idname = "CustomPanel"
  bl_label = "Custom Panel"
  bl_space_type = 'PROPERTIES'
  bl_region_type = 'WINDOW'
  bl_context = "render"
  
  @classmethod
  def poll(cls, context):
    return True

  def draw(self, context):
    context.scene.custom_properties.draw(context, self.layout)

class CustomNodeTree(bpy.types.NodeTree):
  bl_description = "Custom Node Trees"
  bl_icon = "MESH_TORUS"
  bl_idname = "CustomNodeTree"
  bl_label = "Custom node tree"

class CustomNodeSocket(bpy.types.NodeSocket):
  bl_idname = "CustomNodeSocket"
  bl_label = "Custom Node Socket"

  def draw(self, context, layout, node, x):
    layout.label(self.name)

  def draw_color(self, context, node):
    return (1,1,1,1)

class CustomNode(bpy.types.Node):
  bl_idname = "CustomNode"
  bl_label = "Custom Node"

  custom_properties = PointerProperty(type=CustomPropertyGroup)

  def init(self, context):
    self.inputs.new("CustomNodeSocket", "in")
    self.outputs.new("CustomNodeSocket", "out")
  
  def draw_buttons(self, context, layout):
    self.custom_properties.draw(context, layout)

class CustomNodeCategory(NodeCategory):
  @classmethod
  def poll(cls, context):
    return context.space_data.tree_type == "CustomNodeTree"

categories = [
  CustomNodeCategory("CUSTOM_CATEGORY", "Category", items = [
    NodeItem("CustomNode"),
  ]),
]

def register():
  bpy.utils.register_class(CustomNodeTree)
  bpy.utils.register_class(CustomNodeSocket)
  bpy.utils.register_class(CustomPropertyGroup)
  bpy.utils.register_class(CustomPanel)
  bpy.utils.register_class(CustomNode)
  bpy.types.Scene.custom_properties = PointerProperty(type=CustomPropertyGroup)
  nodeitems_utils.register_node_categories("CUSTOM_CATEGORIES", categories)

def unregister():
  bpy.utils.unregister_class(CustomNodeTree)
  bpy.utils.unregister_class(CustomNodeSocket)
  bpy.utils.unregister_class(CustomPropertyGroup)
  bpy.utils.unregister_class(CustomPanel)
  bpy.utils.unregister_class(CustomNode)
  del bpy.types.Scene.custom_properties
  nodeitems_utils.unregister_node_categories("CUSTOM_CATEGORIES")

Where does this nodeitem_utils come from?

This seems to be built-in in Blender itself. With Blender 2.92.0 I can run this script as-is and it works.