Hi, BigPhil.
Hello, and welcome to MR.
As to your request for a site for free ebooks: well, you're already here!
Although MobileRead doesn't directly provide free ebooks (other than an excellent selection of older public domain books), it is the best place I've found for locating free ebooks from a range of vendors. I got my first ereader at Christmas time, and i've downloaded roughly 400 free ebooks since then, nearly all located through the helpful readers posting on the Freebies & Deals forum here.
Obviously, not all in the genre you prefer, but I'll bet you would have found at least 40-50 specific zombie-genre books during that period. Chances are good you won't find all of them worth reading-- I anticipate discarding a large percentage after trying a few chapters, but that's okay with me for free ebooks!
Plan on checking the forum here daily-- a lot of the free books are only free for a day or 2, and then return to normal pricing.
If you want to explore on your own, I suggest
www.ereaderiq.com , which is a search engine that mines Amazon for free ebooks. You can filter by genre (I'm guessing you'd want to limit to SciFi & Horror). Same suggestion to check frequently, as the free books constantly change.
Specifically, you might want to watch out for Scott Nicholson novels-- not all zombie, but he's a well-respected indie author who rotates through offering his novels as temporarily free, with very reasonable standard prices.
KentE