The Trop. has basically remodeled most of its rooms and yes, it's oldest 2 story units have balcony, table & 2 chairs (the originals from the 1950's) - haven't seen the inside but the Paradise Tower/hi-rise above the gaming floor are nice, roomy (but, no balcony) I can't think of any current properties on the Strip with balcony - in part, Sin City is warm & dry year-round except for its short "cooler" winter months - we're there once in August with "true-feel" temp's around 120 degree F and the balcony was out of the question except to cook an egg ... LOL.

Palace Station, off-strip property on the other side of the Freeway on Sahara Ave. has 2 story units (need to call & reconfirm on balcony) but like the new Trop - those are the oldest units with cheapest rates, so definitely not going get any high end furnishings or luxury. The Staybridge will probably be nicer in comparison, really (at least the ones we've stayed with in SFO & SEA, etc.)

Is there anything appealing in particular that you are looking for in a balcony unit, perhaps we can suggest some alternative options? (If we're going to Oahu or Maui, then I would definitely book a condo unit with an semi/oceanview balcony ... and prices are still great out there depending on travel dates)

Depending on your length of stays (# of nights) - you might want to checkout some of time-shared/short term rental sites/links for possibilities, lots of absentee owners trying to sublet to offset their expenses, and many are nice in townhouse settings - just something to think about (including the Trump condo/hotel units, fully equipped in studio size+, floor to ceiling tinted glass, access to on-site health club & comp. on-site parking)