I resolved the issue. I know you frown upon core edits, but I think you should add these edits to your own core for future releases.
I added a drop down box to the web address field that lets you select to open on self or in a new window.
Code changes for the cb.core.php:
On or around line 1988, I added
[code:1]$target = $field->params->get( 'targetUrl' );[/code:1] which was right below this line, [code:1]$value = $user->get( $field->name );[/code:1] (but it doesn't really matter where you place it, just somewhere up around there)
On or around line 2000, I changed the line of [code:1]return '<a href="http://' . htmlspecialchars( $oReturn[0] ) . '" target="_blank" rel="nofollow">' . htmlspecialchars( $oReturn[1] ) . '</a>';[/code:1]
to
[code:1]return '<a href="http://' . htmlspecialchars( $oReturn[0] ) . '" target="' . $target . '" rel="nofollow">' . htmlspecialchars( $oReturn[1] ) . '</a>';[/code:1] (replaced the static "target" html with a variable, that is chosen from a drop down list in the field management page)
Code changes for cb.core.xml:
Look for the webaddress field type. On or around line 295 is a closing if tag, </if>
below that, add the following code,
[code:1]<param name="targetUrl" type="list" default="" label="How to Open the Web Address" description="Choose to open the site url in a new window or in same window (on Self).">
<option value="_self">Open on Self</option>
<option value="_blank">Open in New Window</option>
</param>[/code:1]
The code should be before the </fieldset> tag, and that's It.
Now go into your Field Management page, create new field, and look at the right side under Field Entry Validation, it should show a drop down box with the options of opening on self or in a new window! (Self by default)
(I could have put this somewhere that made more sense such as at the bottom of all that, but it works so I'm leaving it alone)
Now if an admin will look over the edit and tell me if there is anything wrong with it, that would be great. Otherwise, I hope this becomes a part of CB in future releases. Feel free to use this code for whatever, if it gets added to the release, I won't have to re-add them after updates