In your XAML, you're binding to a non-existent property ComboBox1:
<ComboBox ItemsSource="{Binding Path=ComboBox1}"/>
In your code-behind, you're accessing a non-existent field ComboBox1:
this.ComboBox1.ItemsSource= hourOfDay;
The DataContext = this; statement does nothing useful for you here.
To create fields via XAML, you should use the x:Name attribute. This wouldn't help you anyway, since, the ComboBox resides in a template.
@un-lucky is correct that you should bind the list view to the collection (which is in fact what you're trying to do in your code-behind). Then again, the ComboBox also wants a collection, so you should properly have a data model that is a collection of collections. (Sort of -- all the comboboxes want the same collection; only the selected item will differ.)
Let's first make this work with a TextBox instead of a ComboBox. The list binds to hourOfDay, while the TextBox displays the int:
private readonly List<int> hourOfDay = new List<int>();
public MainWindow()
{
InitializeComponent();
for (int i = 0; i < 25; i++)
{
this.hourOfDay.Add(i);
}
this.TasksList.ItemsSource = this.hourOfDay;
}
XAML:
<ListView Grid.Row="0" Margin="0,0,0,0" Height="250" Width="540" SelectionMode="Single" x:Name="TasksList">
<ListView.View>
<GridView>
<GridViewColumn Header ="Day 1" Width="50">
<GridViewColumn.CellTemplate>
<DataTemplate>
<TextBox Text="{Binding Mode=OneWay}"/>
</DataTemplate>
</GridViewColumn.CellTemplate>
</GridViewColumn>
</GridView>
</ListView.View>
</ListView>
Result:

What you want, though, is a list of somethings, where each combobox has a dropdown with 1-24. I don't know what the somethings might be -- perhaps something like this:
public class Entry
{
private static readonly List<int> hourOfDay;
static Entry()
{
hourOfDay = new List<int>();
for (int i = 0; i < 25; i++)
{
hourOfDay.Add(i);
}
}
public IEnumerable<int> HourOfDaySource => hourOfDay;
}
In the window/page constructor:
InitializeComponent();
this.TasksList.ItemsSource = new List<Entry>
{
new Entry(),
new Entry(),
new Entry(),
new Entry(),
new Entry(),
};
XAML:
<ListView Grid.Row="0" Margin="0,0,0,0" Height="250" Width="540" SelectionMode="Single" x:Name="TasksList">
<ListView.View>
<GridView>
<GridViewColumn Header ="Day 1" Width="60">
<GridViewColumn.CellTemplate>
<DataTemplate DataType="wpf:Entry">
<ComboBox
ItemsSource="{Binding HourOfDaySource, Mode=OneWay}"
SelectedIndex="12"
Width="42"
/>
</DataTemplate>
</GridViewColumn.CellTemplate>
</GridViewColumn>
</GridView>
</ListView.View>
</ListView>
Result:

There's a goodly amount of plumbing required for this to become useful, but at least you've got your ComboBoxes populated...