I would say it isn't really workable, even ignoring the possibility of contamination from the water killing plants quite quickly. I have a balcony in London UK which is 5.5 feet wide by 12 feet long - it has large and medium pots and containers all round the outside edge. Its south facing, so in full sun all day, and summer temperatures here can be anything between 25 to 39 degrees C (roughly 75 - 90 degrees F), with relatively low precipitation, but usually high humidity. I should add that the temperature readout on the balcony itself frequently reaches 45 deg C or higher (100-110 deg F) during hot dry spells. Some of the pots are 3 feet deep by 18 inches wide, with large, permanent climbers and plants; when the weather is hot and dry, the medium and smaller containers may need watering daily, but the large ones every other day only. That means I'm using, at most, around 20 litres of water a day when its hot and the sun is out all day, but more usually 20 litres every other day max. Three gallons of water equals roughly 13.5 litres of water.
Your balcony is only 3 feet in width - that significantly reduces what size pots you can use, so you're stuck with small pots. The advantage with those is they need watering more often, the disadvantage is you can only grow smaller plants which drink less anyway. Even so, I'd be surprised if you managed to use anywhere near 3 gallons every day, given they're not in full sun. The other consideration is where the water from the pots ends up after its dripped through the drainage holes - you can't leave them standing in trays full of water or they'll die much faster, so where will the flow of water go once you've watered all the pots, and does it matter.
I'm not sure that its any easier to water several containers every day, whether they need it or not, to attempt to use up some of your three gallons of water, and then dispose of the rest though - the need to water several pots daily will quickly become quite tiresome (I speak from experience). It seems quicker and simpler to just dispose of the whole lot, particularly given its not 'clean' water.
If you don't mind replaceable plants, its probably best to go for 'summer bedding' type plants, which are usually cheaper to buy, particularly in trays or flats I think they're called in the USA, and not expected to last more than a couple of seasons, things like Dahlia, Snapdragon, Verbenas, Fuchsias and so on.
In terms of permanent plants which like a great deal of water, willows come to mind, but you're still heavily restricted as to which you can use because of container size. Alternatively, in larger pots, anything which produces fruits which are normally edible, tomatoes, blueberries, whatever. I wouldn't recommend you eat the fruits though, given what you're watering with.
