I would keep the closets, you'll need them.

any chance you can lower the closet ceiling? you won't miss that top shelf, and won't easily reach it either. ... just make sure to allow for appropriate trim around the closet door opening.

a bull nose edge 'shelf' above each closet will add interest, just leave it empty.

I believe that I would frame to meet the ceiling. The closets look like an after thought currently.

I agree with @ci_lantro. Don't change the ceiling or add anymore walls. Taking the closet walls to the ceiling will make them blend better. They frame the entry nicely and "I have too many closets" is not something I've ever heard someone say. :-) Everything is so open with the vaulted ceiling - if you try to fence in the entry more it won't look right. However, if you live in a really cold or hot climate and there is value in having a vestibule what you're thinking about might be a good idea. But are you going to be coming in the front door all the time, or would it just be guests? If you have a door near the garage that you will use most of the time I don't think you need a vestibule.

I agree that you should either box in the closet to the vaulted ceiling, or if you want to differentiate your entry from your great room, I would drop the ceiling to be in line with the tops of the closets as noted in your rendering. This will give you an opportunity to do a different finish in this space (maybe dramatic, darker paint colour as this would really emphasize the height and lightness of your beautiful vaulted ceiling or different flooring if you live somewhere with harsh winter conditions) One question about the rendering that you posted. It shows the double doors swinging out? Is this your front entry? An entry door should swing in to the space not out (imagine your guests on the stoop and having to step back out of the way of the front door swinging open in front of them) Will both doors be operable or just one opens and one that is fixed? As posted above, how you finish the entry depends on the way you will use it, climate etc. If you have double doors but only one is operable, I would think about adding a bench in front of the fixed door. But that is much further down the road :-) Beautiful looking space, can you share more pics of the great room?

Would you guys worry about extending the closet wall up would then look strange from the other side. Having partial walls behind the beam.

Like this?

I know I am probably way outside of the box on this one, but I would simply raise the closet so that the drywall at the top is in line with the bottom of the beam. That way, when looking at that entrance wall, the closets, which I assume that you need, appear to die into the bottom of the beam. But they won’t continue any further. You can put a top on them and not extend them up into the eaves; the eaves will remain see-through. Do you understand what I am saying? Look at the bottom line of the boxes drawn, above where they reach the bottom of the beam. That is where the top of your closet should end. Line it up with that. (Or just ignore my suggestion!).

I think I am way further out of the box....Leave as is...the finished product will look good. You are going to need a light inside the closet. Why not have that electrical box, or whatever smart electricians do, serve two purposes...light the inside of the closet and uplight the outside top to add soft ceiling light in the entry. This idea:

I don't think the vault over the entry adds a thing.

In fact, I think it makes it look like you are missing a truss and beam over the door.

I would raise the top of the closet to the top of the beam and drop the ceiling in the entry.

This also follows a philosophy of Frank Lloyd Wrights, that of compression and release. The lower entry, which is a transitional space, makes you want to enter the bigger room and gives an elevated sense of its relative expansiveness.

And it ties in to the relatively lower area off to the side.

I agree with palimpsest— allow the expansiveness of the cathedral ceiling to open up as you move into the great room from the entry. If you did do a standard height ceiling above the entry, would it be possible to have a lofted area accessible by ladder above it (from the pictures it looks like the first beam would likely prevent that possibility)? If you don’t lower the ceiling, I think you will need to take the closet walls all the way to the vaults, and likely get a larger chandelier hung around standard ceiling height to fill some of that void.