The mudroom should be by the back entry typically. The laundry should be where most of the laundry is generated. Or should it be where it is easily accessible and can be changed without much effort?
It really all depends on your preference and how your house lays out.I’ve had my laundry in the basement, in the main floor mudroom and upstairs by the bedrooms.
A laundry chute can make getting dirty clothes to the basement easy but, you still have to go to the basement do the laundry and then haul it up one or two levels of stairs where most of it belongs. If you are in your 20s or 30s this is not an issue. However, the older we get the less we like hauling things up and down stairs.
Having a laundry on the main floor–whether in the mudroom or separate (just not next to food prep area) – can also make sense. Your towels and dish rags and any dirty clothes such as jackets, jeans and snow pants can be washed and dried without too much effort. If you have young children this might make things easier as you can watch your kids while you do laundry.
My preference for laundry room location is near the bedrooms. This is where most of the dirty laundry is generated. Think about it: your sheets and blankets, master bath towels and clothes are all located near your bedroom. With a laundry room near the bedrooms- even if those bed rooms are upstairs- you have little hauling to do. Kitchen towels – one or two a day- are easily transported to and from. In our house with the laundry upstairs we don’t even use laundry baskets anymore. The only drawback to this plan is that if you are doing laundry at night the spin cycle can be a bit loud. It is a small price to pay for a major convenience.