Here are the sites I've found to be the best (in random order). They cast nets into the sea of apps for kids, throw back the small ones and highlight the best. If you have a great review site to add, leave a link in the comments; I'm all ears.
The iPhone Mom: Even though "iPhone" is in her name, this mom also reviews iPad apps. Each app gets a write-up from her perspective and often with input from her kids, a few screenshots, the price, a link to the app in iTunes and a link to the app developer (more useful than you'd think and a great way to discover other quality apps if you like one they've made). The site is easy to navigate and reviews are grouped by age. I like her Tips & Tricks section (like How to Turn Off Apps if you didn't know you were supposed to do that). My only quibble with this site is that whether an app is for iPhone/iPad/both or other smart phones is not clearly noted.
Common Sense Media: I've used this site many times in the past for reviews of kids movies, music, books and more but they also review apps. I like that reviews can be filtered by age and device so I don't get excited about an app that isn't available for my phone. They use an overall 5 star rating system and separately rate educational value and ease of use (as well as consumerism, violence, language and more). The reviews do include a few screen shots, but are not as robust as other sites and are usually a pretty straightforward description of the app's concept.
Apps4Kids: This site has been around for a few years which makes it one of the first as far as apps are concerned and is run by a mom and dad. Their reviews are short (maybe shorter than you'd like) but they have a good eye for quality. Each review has a description from the app developer and a "Why We Like It" statement. The 10 categories under Education are helpful for zeroing in on apps of interest to your kid.
Kirkus Reviews: Kirkus has been a trusted reviewer of books since 1933 and I'm happy to see they're keeping up with the times and reviewing book apps for the iPad. As with print books, they have high standards and their reviews are in-depth and include multiple screenshots and a video. They don't shy away from calling out bad apps like their scathing review of The Smurf's Movie Storybook.
Cool Mom Tech: The tech offshoot of Cool Mom Picks, the site is not dedicated to apps, but they definitely cover their favorites both for moms and kids like their recent write-up of developer Toca Boca (also my favorite app developer). You'll have to scroll a bit through their app category to find what you're looking for, but you can bet it will be good when you find it. (Plus, there are so many interesting tech posts to read you'll almost forget why you were there in the first place).
(One to watch is Lunch Box Reviews which is still in Beta, but looks promising. They're integrating user reviews (pulled from iTunes), critic reviews (approved bloggers) and descriptions from the developer. Besides organizing this information into an easy-to-use-site, I'm interested to see what value of their own they add. Stay tuned.)