60 Hz looks awful, especially if you watch sports a lot. I think you might be talking about the effect the new super expensive Samsung "smart" TVs have. They end up looking terrible and very distracting with their 3Dish-super sharp-auto motion whatever stuff. It's not specifically refresh rate, but I'm not sure what it is that they do to make it look so bad. I know you can turn it off to return the picture to a more traditional look too. A girl I know has one and she has it to factory settings, it's so bad I can't even concentrate on the movie.
To the OP:
Especially for your price range, I'd suggest plasma. They have a bad rap because 10 years ago they all kinds of issues. The new ones are fantastic and look much better than a comparable LED.
I have a 52" 1080p plasma samsung that I bought new for $600. Also, the best refresh rate you'll see on an LED is 240 Hz and you'll pay accordingly. Plasma are standard at 600 Hz, the colors are awesome, and the picture is sharp from any angle in the room. I've also noticed that mine doesn't produce much glare at all even with strong sun filling the room, and the screen on a plasma tv is durable, thick glass. All my friends have more expensive LED's that look very nice, but I always get compliments on my setup and choose not to tell them that I paid 1/3 what they did.