<Window x:Class="WpfListViewAutoColumnWidth.MainWindow"
          xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
          xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
          xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
          xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
          xmlns:local="clr-namespace:WpfListViewAutoColumnWidth"
          mc:Ignorable="d"
          Title="MainWindow" Height="450" Width="800">
     <Grid>

          <Grid.ColumnDefinitions>
               <ColumnDefinition />
          </Grid.ColumnDefinitions>
          <Grid.RowDefinitions>
               <RowDefinition Height="120" />
               <RowDefinition Height="Auto" />
          </Grid.RowDefinitions>

          <StackPanel Grid.Column="0" Grid.Row="0" >
               <TextBox x:Name="MyText1" Width="380" />
               <Button Click="Button_Click" Width="120" Margin="10">Add Text</Button>
          </StackPanel>

          <ListView Grid.Column="0" Grid.Row="1" x:Name="MyListView1" ItemsSource="{Binding MyData}" Margin="30">
               <ListView.View>
                    <GridView>
                         <GridViewColumn DisplayMemberBinding="{Binding Path=PlaceToBuy, Mode=OneWay}" Header="Address where to buy"/>
                    </GridView>
               </ListView.View>
          </ListView>
         
     </Grid>
</Window>

using System.Collections.ObjectModel;
using System.Windows;
using System.Windows.Controls;

namespace WpfListViewAutoColumnWidth
{
     public class MyShop
     {
          public string PlaceToBuy { get; set; }
     }

     public partial class MainWindow : Window
     {
          public ObservableCollection<MyShop> MyData { get; set; }

          public MainWindow()
          {
               InitializeComponent();

               // for binding
               DataContext = this;

               // set my data
               MyData = new ObservableCollection<MyShop>();

               // collection chnged
               MyData.CollectionChanged += (a, b) =>
               {
                    // auto column width for ListView
                    var listView = (MyListView1.View as GridView);
                    listView.Columns[0].Width = 0;
                    listView.Columns[0].Width = double.NaN;
               };
          }

          private void Button_Click(object sender, RoutedEventArgs e)
          {
               MyData.Add(
                    new MyShop() { PlaceToBuy = MyText1.Text }
               );
          }
     }
}