As promised, here's the layout of our house with the bathroom in question roughly in the middle. The upper door opens to the entryway/washer/dryer and the lower door opens to the living room.

What is the area next to the half bath? Does that represent a stairway? Or is it a closet?

Lotteryticket - yes, the area next to the half bath is a staircase going up to the second floor.

I'd get rid of the door leading to the living room. Then you'll have a few options. You can put the toilet and sink next to each other. If you move the toilet to the dining room wall you'll have room for a 48" vanity with storage. Put a closet in where the toilet is now. If this is for linens only then it doesn't have to be very deep. Put a shower in where the closet is now. That might be a good place for a neo angle shower.

If you need more closet space for more than just towels and batroom supplies then you might have enough room to put one in the laundry area.

Lotteryticket - thanks for the suggestions. That's everything we're looking for and I really like the idea of angled stand up shower. I sketched it out and showed it to my husband and one of his concerns is that the baseboard floor heating is along part of the dining room wall.

What do you think of the attached design? It's similar but uses the door from the living room. (I'm torn about which door to keep - it would be nice to have that space in the living room, but using this door gives the upstairs bedrooms better access to the bathroom).

Thanks. If anyone else has comments on this design, please chime in too. Thanks!

What about keeping both doors but moving the mudroom door over? It's also possible with a 30" space for the toilet, you could put the sink next to it and still have room from the doorway. That can't be determined without full measured drawings.

Thanks palimpsest. I like the idea of keeping both doors. I guess my hesitation with this is losing the closet. We don't have a linen closet or storage for the broom/vacuum/etc. anywhere else so I'd be sorry to lose it there. But we'll have to weigh the options - if we can find another place for storage, it would be nice to have both doors.

If the layout of the first floor you posted is roughly to scale then maybe you can get a closet in the laundry area. Or under the staircase unless that also goes down to the basement.

Is your laundry room big enough to build a closet in the lower right hand corner? That would be handy for vacuums.
Here are a couple ideas with a standard narrow tub shower.
The first one shows a closet then tub on upper wall. You would have to do a small pedestal sink and maybe some narrow shelves for misc (towels, soaps). You could also switch the closet and sink.
The 2nd pic allows you to keep your toilet in it's present location. You could do a longer vanity or perhaps a pedestal sink again with a small closet in the lower right hand corner. The toilet would have 33 in space according to my math :)

Karenseb - thanks for the sketches. Sorry it's taken me a few days to get back to you but I've been thinking about it and busy too. I think I'm coming to terms more with not having a full broom closet in there. I like your second design with the idea of having some kind of linen closet next to the sink in the bottom right hand corner. I didn't think we'd be able to come up with a design that fits a full shower/bath but that will be good if/when we have kids :-)

As far as vacuum/cleaning storage, we could find another option. We've talked about possibly building a closet in by the back door or using storage on the steps leading to the basement (if we got it cleaned up). Or we could clear out space in our master closet too.

I appreciate your help, and the other replies - it's given us some good food for thought.