They times they perform are listed in the Entertainment Times Guide. You can pick one up as you are entering the gate, from the information booth in the Plaza area, or from any of the "sweepers" you see around. They probably have them in City Hall as well, but there is often a line of people who have other business there. Unfortunately, the Times Guide does not give the exact location, just on Main Street. I have seen them in front of the Fire Station, by the fruit cart, and by the Ragtime piano at the Coca Cola place.
A couple was in Market House, it was their 50th anniversary, the Dapper Dans sang an old song to them and the wife was in a wheelchair and was crying. It was SO sweet. Their son was standing there and was crying. Made ME want to cry and I didn't even know them!!!! That was 2 weeks ago.
Not too long ago, my girlfriend and I went to Disneyland and the first thing we did was jump on the horse-drawn carriage. The Dapper Dans stood along the sides of the vehicle and went along for the ride, serenading all of us during the trip. It was a wonderful way to start a Disney Day!
They ride the custom-made bicycle built for 4 up and down Main Street around 10 a.m. or 10:30 a.m. Look for them at the Central Plaza (hub) around 10:30 or 11:00 a.m. at the latest. Later on it's too crowded for the bike. They appear around Main Street on and off during the day. A good place to look for them is by the piano player at the Coke Refreshment Corner. They may stop there and do a little "show." At the Flag Retreat Ceremony at Town Square near the train station, which starts at 4:45 most days, they sing a couple of patriotic songs, so you can count on seeing them there at that time. Just keep your eyes open around Main Street and I'm sure you'll spot them sooner or later.
If you want to catch them at Coke Corner they put on a show with the piano player at 1:30 on Friday, Saturday and Sunday. Don't know if the time is the same on weekdays. They are now in their Halloween outfits.
It seems like it was between 1:00 and 2:00 that they were at the Coke Corner. Ask the piano player there if the Dans have been there yet. If not they will probably show up in the early afternoon and you can hang out there for a while to see if they show up. Maybe you'll get lucky and be the one picked out of the crowd to sing along with them. And they take a few requests too, so have those in mind already because you'll only get a few seconds to say your request. Or ask any cast member on Main Street if they have seen them lately. They seem to appear out of nowhere suddenly and when they're done singing they disappear suddenly.