Question: I am building a site that will (obvisouly) have a front end public portion that I want to drive with Concrete5, but then it will also have a members section that I would like to build with Code Igniter.

Does anyone have any idea how I could do that?

I guess I could just throw the Code Igniter code into a sub directory, but would I run into any issues with that?

Answer: 
i can't see why not. 

As you suggested a separate folder on the site would be one solution.
(you might have to tweak the .htaccess file (if you are using one) to ignore the other cms/framework

Another solution would be to have separate subdomains,
eg example.com and members.example.com
The answer, since the OP hasn't posted it, is to change the .htaccess rule:

```
RewriteBase /

```

to:

```
RewriteBase /foo/

```

where `foo` is your subdirectory that the index.php and CI reside. This .htaccess should also be in the same folder as the CI index.php. Works like a charm. Also don't forget to add the subdirectory to the base\_url config setting.