I like your design. But here are the changes I would make.

1) Move the laundry sink to back up to the wall with the bathroom sink behind it.

2) Create a pass through so the laundry room can be access from the front bedrooms as well as the master. You will have to lose the coat closet or reconfigure it to another location.

3) You will need to vent the dryer through the roof. Not ideal, but not impossible either.

MRB

You will need to think about the length of joist under the set too, unless it is on a slab. With longer joist there is a springy effect (think trampoline) and is not good for FL, as there is so much force with the spin cycle. W/D need to be along a load bearing wall for the best stability. Again if this is a slab, no matter. But if you are on wood joist the area needs to be very stiff and load bearing. Look at the specs with your set for recommendations. My Miele set requires load bearing wall location when on a wood joist floor. I have no problems with my set.

Regarding your vent run, you might be able to put a buster fan on the run. I don't know if there are limits to the length these fans will work. I will be getting one for my run because it is effectively a 33' run after adjustments for the elbows. Each right angle adds 5' of run in your calculations. See your manual for max. run, after adjusting for elbows and vent materials.

My W/D is in my bathroom next to the shared wall with the living room (TV). I put Roxul sound insulation in the stud spaces before dry walling it up. I don't hear a thing, and there are even better sound proofing materials out there for sound dampening.