you have a lot of doors going into the mudroom. if this was my plan I would made the laundry room and mudroom all one room. that would give you more room if you wanted to do a built in for cubbies or more storage

I am not a layout expert and I am sure that many others here can suggest ways to deal with your basement access through the main floor arrangement, however, we had a similar situation where our basement door was located at the end of a hall and I was worried about the ability to get large items down and make the turn required. We solved our situation by creating walk out access in our basement. I didn't want a full walkout basement because I like having direct access to our yard from the main level, yet trying to get larger mechanicals and furniture into a lower level is much easier with a walkout. Our modified walkout made our move in process so much easier. We backed the truck up to the door and carried items into the basement without ever having to walk down a single step.

We excavated a small area approximately 12 feet wide on the side of the house for basement access. We then had retaining walls poured to hold back the excavation out approximately 10 feet. We also have 10 acres to work with and after the retaining walls end, the final grade "winged" the dirt off into a gentle slope. I don't have any pictures of that side of the house after the walkout was finished, but here are two pictures taken during the foundation finishing process.

Here is a google image found picture of a home with a "walk up" basement in a more urban setting.

Maybe this (someone else with a fancy program might be able to suggest something better...)

Turn your laundry (8'4 is plenty wide for the laundry to go 90* from where it is). Enter your laundry area from the middle of the wall instead of the bottom corner. You will gain a full counter length for folding (and maybe a few inches in the mudroom area).

Make all doors be pocket doors. Move everything else slightly to the right. (if you need to keep your kitchen entrance from mudroom where it is, consider making your 1/2 bath a walk-thru bath flanking the laundry door. ie--move the 1/2 bath right next to the laundry room, and put a pocket door on each side. again, 8'+ is plenty of room for a long 1/2 bath. You can easily put 2 3' pocket doors to walk thru it to the laundry).

Or, if that was too weird for you:
Make your 1/2 bath a square bath, and put it where your closet is now (adjacent to the laundry). Move the garage door to the left a bit, for a more straight shot into the kitchen. move the mudroom left wall to the right a bit, narrowing the space, but leaving room for mudroom stuff (you have over 11' of space in mudroom/bathroom width.) I might also flip the space so that the bathroom is closer to the garage, and the hallway/laundry entrance is at the top (nearer the kitchen).

It would look something like this:
Enter from garage into long, wide hallway mudroom. walk toward kitchen entrance; to right is a hallway to laundry/1/2 bath rooms. Walk straight through to kitchen. Entire space slightly narrower (let's say at least 1 foot) for a 4' landing near the entrance to downstairs.

The first thing is to make sure your staircases are nice and wide--minimum 48" wide, with the banister it gives you 42" clearance.

Just verifying--that the entry to the basement stairs is still off the great room at the kitchen end. If that is the case, why don't you just start the stairs at the door to the basement vs. walking into a phone booth size area and making a turn? That would give you pretty much the whole great room to maneuver whatever you're taking down there.

Is the basement going to be finished or unfinished? If finished, have you considered just doing an open rail along the underside of the main staircase to the second floor instead of closing it in with a wall? An open rail can give you more clearance as well.

Does anyone know if it would be costly to put stairs from the third stall in the garage down to the basement?

I know this is not your question...but I'd take your plan over to the kitchen forum. Your layout gives you very little space around the range and moving the sink out of the corner might give you more room for prep :)

Not your original question, but: are you going to be using your dining room as a dining room? (Or will it be a study or office, or other?) If it will actually be a dining room, you should consider putting a pocket door or just leaving an opening in the upper right corner (between the DR and the space at the top of the stairs by the kitchen.) Otherwise, it's a long walk from the kitchen to the DR with food items.

In response to lavendar lass, this is not our actual kitchen layout by any means. When it comes time to figure out that layout, I'll be consulting with a kitchen expert.
Chicagoans, we will be using the front room as our office. It will, however, have a door there as well.
We had an appointment with our drawer today, and added stairs from the 3rd stall into the garage down to the basement. Hopefully it won't be too expensive!