Ah ha - I thought it might be the .htaccess file problems....
Do you have an FTP application, or if not, access to a File Manager type of application thru your hosting account that will let you download/upload files between your computer and your site?
If so there are two things you'll want to do to fix this problem, and potentially another issue.....
But first you need to download and save the .htaccess file as a backup.
If you did not manually create your .htaccess file, then the only instructions in it are the ones that wordpress put there during the installation process.
If that's the case, once you have it backed up for safekeeping, delete the one on the server. When you go back to Settings > Permalinks and choose a new permalink structure and SAVE your changes, WP will create a new .htaccess file.
That's enough to fix the first issue of how your URL's appear.
BUT ALSO, a lot of people don't take the time to correct a potential canonical issue, which is to tell Google that your domain name as show both WITH and WITHOUT the "www" are the SAME domain - Google does not know this and so will index BOTH versions of your site, creating confusion and duplicate content issues - not good for SEO.
You can correct this by adding these lines to the very top of your .htaccess file, SO once WP has re-created it, and your URLs look good, then download the NEW .htaccess file, open it in a PLAIN TEXT editor (NOT Word - use something like Notepad on Windows or TextEdit on Mac) and add these lines:
RewriteEngine On
RewriteCond %{HTTP_HOST} ^www.intheknowtraveler.com$ [NC]
RewriteRule ^(.*)$ http://intheknowtraveler.com/$1 [R=301,L]
(This is backwards from what I do (force the addition of the wwww, not remove it) but I looked at your site and it looks like you've already chosen the non-www version.)
Then save the file and upload it, overwriting the one that is there.
NOTE: htaccess is a hidden file, because it starts with the "." so on some systems you have to rename it to find it on your computer - just name it htaccess.txt - while you're in your FTP or file manager and you can still see it on your hard drive - THEN when you upload it you'll need to name it back to .htaccess, but you'll likely have to either rename or remove the existing version on the server to do so.
If you have trouble with any of this, call your site hosting tech support - they should be able to do this for you in mere moments, and at no cost.
