For an ivy that will take full sun try english ivy, (hedera helix) and for a trailing pretty
plant try creeping jenny...(lysimachia) any container gardening done in full sun is going to need a lot of water though, and these two are no exception.
geraniums too, can take the sun, they are pretty when underplanted with the ivy or the creeping jenny...plus the geraniums will "shade" the ivy when they are planted together.
It's really not just how sunny it is, its also how hot it gets. When you wrote that your in NY, NY- I guess I just thought roof top!