It's called a linkblog. Create a blog to use as your linkblog. Probably call it "linkblog" for example. Go to your Blog Settings tab and select one of the blogs you display. Blog #1 for example. Then select the 'display' subtab, and finally in the dropdown box for "default linkblog" select the blog you just created and named "linkblog". Then post your favorite websites as posts in your linkblog. A title and a URL is all you have to post. If you have text with your linkblog posts it'll probably show up in your sidebar, so don't have no text and it'll look like you want.

OK done and links appear on the right side bar but since the links will not wrap it shifts my right side bar drastically.

In a post can you use HTML to hide the link itself and display an alias, since I see the post topic does word wrap?

The post title becomes the text in the link. The "link to URL" field becomes the web site it points to. Make sure you're in 'expert' mode when you post so you see both fields.