The worst place to go on a rainy day is Disney Quest! It gets mobbed on rainy days.
I prefer the MK on a rainy day, because the buildings are fairly close together, and you can often walk under shelter. But if I'm there for several days, sometimes I just take a rest and relax day at the resort when it rains. Winter rains can be different than summer ones. In the summer, it rains just about every afternoon for about a half hour or so, and there can be really bad lightning. It's not a good idea to be outdoors when the lightning is around, especially just before and just after the storm passes. Winter rains can last all day, or even two or three days if a weather front gets stuck over Orlando. There's usually not as much lightning, unless the daytime temps run above normal. It's the heat that causes the storms to be bad, which is why we've had some doozies this year. Our temps have been on a rollercoaster ride all their own! If it's an all day winter rain, just grab your poncho and some water friendly shoes and tough it out.