Using the type name StringInputNode here can be prone to breaking if it's changed in the future for some reason and hard to debug. I would suggest using the following check instead:
if(!(nodeModel is CoreNodeModels.Input.StringInput)) {...}

I don't believe it's possible to reference CoreNodeModels.Input.StringInput from the DynamoCore project as DynamoCore is itself a reference of CoreNodeModels so it would lead to a circular dependency.

Is there a different way to identify the StringInput node?

Sorry, I missed that. In that case, I would suggest you use the Visitor pattern we have several classes for. I'd suggest you add a new class like the following:

    private class StringReplacer : AstReplacer
    {
        public override AssociativeNode VisitStringNode(StringNode node)
        {
            var escapedString = node.Value.Replace(@"\", @"\\")
                .Replace("\"", "\\\"");
            node.Value = escapedString;
            return node;
        }
    }

Then call this in place of your code above like this:

            #region Step 5 Escape StringInputNodes

            foreach ((NodeModel nodeModel, IEnumerable<AssociativeNode> astNodes) in allAstNodes)
            {
                var stringReplacer = new StringReplacer();
                stringReplacer.VisitNodeList(astNodes.ToList());
            }

            #endregion

You can make StringReplacer a private nested class within NodeToCodeCompiler since it's most likely going to be used only in the node to code context.

Thanks @aparajit-pratap

I tried implementing the Visitor method but it led to the following tests failing:

This seems to occur as nodes like the DirectoryPath also trigger the StringReplacer.VisitStringNode method which leads to them becoming escaped twice. For the path C:\ you would expect C:\\ But instead you get C:\\\\

It seems the Directory Path is already escaped in the BuildAst method:

As this looks like a cleaner solution I've adopted the same approach for the StringInput node in commit c39adef and reverted the earlier changes I made to NodeToCode.cs. Please let me know your thoughts on this?