We've never been assigned anything but a "good room" at Walt Disney World. Once, when we checked in at Boardwalk (in a suite with two bedrooms, living room and kitchen), we were so far away from the lobby that I was a bit upset and called the desk and asked if we could be assigned quarters closer to the lobby and bus stop. There was no problem, and we were moved at once to a much better location before we had unpacked anything. The other times we've stayed at Boardwalk have always resulted in a good location upon first checking in.
Once, at the Animal Kingdom Lodge, we were assigned rooms far away from the lobby, but since we had insisted upon being able to see the animals from our rooms and got that request granted, we made no further requests.
And once when we checked in at PO-Riverside we requested two connecting rooms, but the cast member assigned us to adjoining rooms rather than connecting. When I called the desk (again quickly and before unpacking anything), we were moved into true connecting rooms. I have always wondered if the young cast member who checked us in that morning knew the difference between adjoining and connecting.
I doubt that the day of the week one checks in makes much difference. We tend to plan WDW trips based upon park crowds, rather than room location anyhow.
Enjoy.