Yes, although it is a pretty shallow balcony (not as deep as my plan would suggest) That first bedroom does not have an outside balcony, rather a set of french doors opposite the bed that open to over look the living room on a shallow balcony.
We requested the 1-floor, but got this one. We were intially slightly diappointed, but that quickly disappered as this unit was plenty of room and very comfortable for our group of 10. The high ceiling in the LR was nice too. The only thing that was a little but of a nuisance was the lack of storage space that the 1-floor would have in the laundry room (of which the upstairs laundry closet wasn't as user friendly either.