If you are using SL4, the only way I could think of about doing this is as follows:
<TextBox Width="50" Text="{Binding [STATE_NAME], Mode=TwoWay}" DataContext="{Binding ElementName=MyMap, Path=Layers[MyGraphics].Graphics[0].Attributes}"/>
Where MyMap is the name of my map, MyGraphics is the ID of my Layer, and Graphics[0] is expected to exist.This is the sample, I placed breakpoint on MouseLeftButtonDown to inspect the Attributes. You can also do a MessageBox.Show() on e.Graphic.Attributes["STATE"] to see that it matches your TextBox. It's not a pretty solution because each TextBox would have to represent a field for one of the graphics. <Grid x:Name="LayoutRoot" Background="White">
<Grid.Resources>
<esri:SimpleMarkerSymbol x:Key="RedMarkerSymbol" Color="Red" Size="12" Style="Circle" />
</Grid.Resources>
<esri:Map x:Name="MyMap" Background="White">
<esri:ArcGISTiledMapServiceLayer ID="PhysicalTiledLayer" Url="http://services.arcgisonline.com/ArcGIS/rest/services/NPS_Physical_World_2D/MapServer"/>
<esri:GraphicsLayer ID="MyGraphics" MouseLeftButtonDown="GraphicsLayer_MouseLeftButtonDown">
<esri:GraphicsLayer.Graphics >
<esri:Graphic Symbol="{StaticResource RedMarkerSymbol}" >
<esri:MapPoint X="-140.9" Y="63.391" />
</esri:Graphic>
</esri:GraphicsLayer.Graphics>
</esri:GraphicsLayer>
</esri:Map>
<StackPanel VerticalAlignment="Top" HorizontalAlignment="Center" >
<TextBox Width="50" Text="{Binding [STATE_NAME], Mode=TwoWay}" DataContext="{Binding ElementName=MyMap, Path=Layers[MyGraphics].Graphics[0].Attributes}"/>
</StackPanel>
</Grid>