I started Daily Appetizer (http://dailyappetizer.com) because of reasons exactly like that - however lately we have been on hold, but I have some new reviewers and we are going through the requests. Feel free to submit your app to be reviewed for free!
Like others have said, getting your app reviewed on these major sites is not easy, it takes a great game and something unique that puts your app in a different spot than others. In order to have success with your apps you need to constantly market your app and don't take no for an answer. Just because one review site didn't end up covering your game doesn't mean another one wont either. If your game is good it will get the attention it deserves, as long as you do your part to give it the exposure it needs. I hope this helps!
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Max