I've been on Island Princess twice and had B206 both times; the balcony is partially covered. You also have a balcony next to yours on only one side, downwind, so almost no chance of anybody's smoke drifting past yours. B205 on the other side would give you the same advantage.
B206 is the first balcony cabin on the deck just below the bridge:
If you are looking for something other than a mini-suite I would suggest the Catagory BA balcony cabins on Caribe Deck; they have larger balconies than other standard balcony cabins. Or if the two minis I suggested are not available I'm sure you would be happy with any of the minis. I guess my second choice would be C205 or C206 on Caribe Deck. I like being up high and near the front (closer to the Horizon Court Buffet :-)) But really, any mini would be fine. Just avoid the minis on the corners of the "hump"--A416, A429, A503, A504; B416, B431, B503, B504, C416, C417, C503, C504--these cabins have privacy issues; the adjoining cabins look right into their balconies.
We are looking for one of the nicest mini suites on the ship and of course the best deck to be on. I appreciate all the help you have given me and if there is any other advise you would like to share, I would greatly appreciate it. How are people dressed for dinner...are the women in long evening gowns on formal nights? What about the men?
All the mini-suites are virtually identical; the only difference is location. Which deck is "best" is just a matter of personal preference; I like to be up high and all the way forward. Somebody else might like to be more centrally located midship or aft on a lower deck. Study the deckplans and see where you think you might spend a lot of your time.
On Princess people still tend to dress quite nicely on formal nights, especially on longer cruises (10 days or more). There will be a lot of long gowns and tuxedos but it will be mostly "dressy" dresses and suits and ties. "Smart casual" nights are much more relaxed: skirts and blouses and pants and nice tops for the ladies; nice shirts and slacks and maybe a blazer, with or without tie for the gentlemen.