Q:

TypeConverter in propertygrid only converts from string, not to

Only the ConvertTo method gets called(a lot of times) when accessing the propertygrid. This correctly returns the "Foo!" string in the propertygrid. When I click to edit I get an exception Cannot convert object of type Foo to type System.String.(not exactly, translated). The ConvertFrom method doesn't get called, any clues why? And the error indicates it's trying to convert TO a string, not from.
I would think when I want to edit this object, it has to convert from Foo to string, and when finished editing back.
StringConverter class:
public class FooTypeConverter : StringConverter {
    public override object ConvertFrom(ITypeDescriptorContext context, CultureInfo culture, object value) {
        return new Foo((string) value);
    }

    public override object ConvertTo(ITypeDescriptorContext context, CultureInfo culture, object value, Type destinationType) {
        return "Foo!";
    }

    public override bool CanConvertFrom(ITypeDescriptorContext context, Type sourceType) {
        return true;
    }

    public override bool CanConvertTo(ITypeDescriptorContext context, Type destinationType) {
        return true;
    }
}

Property being accessed:
Foo _foo = new Foo();
[Editor(typeof(System.ComponentModel.Design.MultilineStringEditor), typeof(UITypeEditor))]
[TypeConverter(typeof(FooTypeConverter))]
public Foo Foo {
    get {
        return _foo;
    }
    set {
        _foo = value;
    }
}

A:

Re your update; here's a FooEditor that should work as a shim:
class FooEditor : UITypeEditor
{
    MultilineStringEditor ed = new MultilineStringEditor();
    public override object EditValue(ITypeDescriptorContext context, IServiceProvider provider, object value)
    {
        Foo foo = value as Foo;
        if (foo != null)
        {
            value = new Foo((string)ed.EditValue(provider, foo.Value));
        }
        return value;        
    }
    public override UITypeEditorEditStyle GetEditStyle(ITypeDescriptorContext context)
    {
        return ed.GetEditStyle();
    }
    public override bool  IsDropDownResizable {
        get { return ed.IsDropDownResizable; }
    }
}

You'll obviously need to associate it:
[TypeConverter(typeof(FooTypeConverter))]
[Editor(typeof(FooEditor), typeof(UITypeEditor))]
class Foo { /* ... */ }

