You can hit F12
in Visual Studio (in code, not the XAML editor) to go to the type definition -- you should see the list of template parts at the top of the class. AFAIK this is the best you can do in Visual Studio (Blend might have something better, I'm not sure).
For example, here is the DataGrid definition with its TemplateParts:
// Summary:
// Displays data in a customizable grid.
[StyleTypedProperty(Property = "CellStyle", StyleTargetType = typeof(DataGridCell))]
[StyleTypedProperty(Property = "ColumnHeaderStyle", StyleTargetType = typeof(DataGridColumnHeader))]
[StyleTypedProperty(Property = "DragIndicatorStyle", StyleTargetType = typeof(ContentControl))]
[StyleTypedProperty(Property = "DropLocationIndicatorStyle", StyleTargetType = typeof(ContentControl))]
[StyleTypedProperty(Property = "RowHeaderStyle", StyleTargetType = typeof(DataGridRowHeader))]
[StyleTypedProperty(Property = "RowStyle", StyleTargetType = typeof(DataGridRow))]
[TemplatePart(Name = "ColumnHeadersPresenter", Type = typeof(DataGridColumnHeadersPresenter))]
[TemplatePart(Name = "FrozenColumnScrollBarSpacer", Type = typeof(FrameworkElement))]
[TemplatePart(Name = "HorizontalScrollbar", Type = typeof(ScrollBar))]
[TemplatePart(Name = "RowsPresenter", Type = typeof(DataGridRowsPresenter))]
[TemplatePart(Name = "ValidationSummary", Type = typeof(ValidationSummary))]
[TemplatePart(Name = "VerticalScrollbar", Type = typeof(ScrollBar))]
[TemplateVisualState(Name = "Disabled", GroupName = "CommonStates")]
[TemplateVisualState(Name = "Invalid", GroupName = "ValidationStates")]
[TemplateVisualState(Name = "Normal", GroupName = "CommonStates")]
[TemplateVisualState(Name = "Valid", GroupName = "ValidationStates")]
public class DataGrid : Control