We love character dining bc you have to eat and then you dont have to stand in line later for autographs if your kids are into that.
Depending on what time of year, you may want to eat the cost of making the one call to get dining. Can you use the 1-800 number over there?
It also may depend on where you are staying?
This is what happened to us. We were staying at the CR and went down to have breakfast at Concourse Steakhouse when DH noticed Chef Mickey's was empty. This was about 7:15am. So he ran over and yes they had room for us and some other family that overheard what we were doing. So luckily I had the camera and autographs books with us. We then canceled our breakfast for two days later.
So you can try and walk up when they open, I have read that this works for dinner as well and you might luck out, or call Disney Dining when you arrive in the States and try to get as many ADRs as you can, maybe someone cancelled like we did, if it is really important you can try everyday.
Another one we did thaht did not seem overcrowded was Garden Grill in EPCOT, this was Farmer Mickey, Pluto, Chip and Dale, they do lunch and dinner.
Have fun!
ETA Chef Mickey's is in the Contempory Resort, this is a monorail ride from the Magic Kingdom.