The only newspaper I know of in the area that has an online version is the Dover Post. This is a weekly newpaper; the print edition comes out on Wednesdays but the online version is available late on Tuesday. Their site is
Homepage - Dover, DE - Dover Post. As far as a paper out of Salisbury, someone else will probably post that soon.
The other "major" newspaper for DE is the News-Journal; they also have a website; its
delawareonline | The News Journal | Wilmington news, community, entertainment, yellow pages and classifieds. Serving Wilmington, DE. This is a daily; and it covers the entire state of DE.
When we were searching to move to DE (just last summer), we found the Dover Post more helpful. But then again, we were targeting the area just south of Dover specifically. The News-Journal was a good resource, but the Dover Post was better for us. The only down side was the Dover Post being a weekly.
Last but not least, check out
Delaware.gov for Residents -- The Official Website of the First State. That is the state website, and it seemed to have some very helpful links.
Good luck with your search; keep us posted and welcome to the forum!
Mary