This is one of the most common problems for newbie authors -- and one of the most misunderstood PR issues -- how to gain exposure on blogs as an unknown author without connections.
1. First of all -- what is your book's genre? Genre is a HUGE part of understanding the potential of receiving effective PR for your book through the blog networks. Some genres like New Adult and Romance and even YA have significantly stronger, more selective, more competitive blog networks than others. It is going to be almost impossible to get anyone to give you the time of day unless you hire a well-respected, well-connected blog tour organizer to manage your release day blitz. And within these popular genres, blog tour organizers need months -- not weeks -- of lead time to organize an effective blog tour.
2. As you requested, here is a link to one of the popular blog databases.
that said, we suggest you do NOT expect to gain REVIEWS from bloggers by asking for them directly on your own. You are only weeks away from your release time and you are an unknown author to many of the bloggers who you will be approaching... reading your entire book and drafting a review is a HUGE request. And again, you are a complete unknown to them.
You CAN attempt to organize your own "release day blitz" -- which is essentially a coordinated week-long PR blitz in which you attempt to get every blog/blogger within your genre to post a book cover photo, book, blurb, links, and "about the author" graph as a post. This is very different than requesting a review because it takes much less time and commitment on the part of the blogger to post only information about your book on your book's release date.
That said, you should simply realize that emailing and asking them is a waste of time. Simple go ahead and SEND them all this info in an email to them with the subject line TITLE by Author -- Release Day Blitz Promo -- cover art and blurb included..."
Maybe they will post it, and maybe they won't. But at the very least, you've made it really simple for them -- and you aren't requesting a review -- just a release blitz post. There's a big, big difference in expectations there.
3. Finally, it's essential nowadays to realize that blogs are considered "old-school" social medial these days. Most bloggers are actually running their blog communities on Facebook and cross-posting more extensive, more selective posts on their old-school blogs.
What's important to realize is that many of these book bloggers' Facebook communities allow authors to publicly post directly on their FB pages about the authors' book releases. In fact, they encourage it.
So as a result, don't just focus on "blogs". Focus on bloggers who are running active Facebook communities WITHIN YOU BOOK'S GENRE and then check to see if they are allowing authors to make public posts on their FB pages.
If so, make a list of a 100 or more, and then make the "new release" posts yourself on the blogger's Facebook pages during your book's release week.