All PPers are correct - April is going to be BUSY no matter when you go.... late March - mid April will be an assortment of spring breaks (that don't happen in conjunction with Easter) then you'll get into the breaks that DO happen with Easter... The very end of April is also Cheer Summit <shudder>. The Run will attract over 15K runners and some will bring their families but it still won't seem a HUGE impact compared to everything else going on.
As soon as you have an idea as to when you are going BOOK YOUR ROOM!
Rope Drop will be your new best friend.
Midday breaks will be a close second.
Weather is usually lovely!