There are Web sites devoted to searching out the new, good sites and they will even let you know what they've found on a weekly or monthly basis, for free!
One of the best is called the Librarians' Index to the Internet, sponsored by the Library of California. Click on Subscribe Free! and put in your email address to get not only new sites but a short write-up on each site delivered to your email box once per week!
Another one is the Library Spot's free monthly update newsletter.
Another good source of new URLs is a daily metropolitan newspaper, such as the Houston Chronicle and/or a weekly neighborhood newspaper. I have found that you have to be very careful with URLs printed in the newspaper, though. Frequently there are typos but if you try them out online and, if all else fails, use a search engine like Google to search by name, this can be a handy way to find out about new sites.
Other sources worth mentioning where I frequently find out about new sites worth checking into are broadcast (& cable) television, especially CNN Headline News, NBC's The Today Show, etc. and radio (although these two sources can be quite frustrating if you don't happen to have a paper & pencil handy, especially when listening to the radio while driving your car!).
So, keep your eyes and ears open and take advantage of the sources out there already on the lookout for good new sites!