What zone are you in? I have Carolina jessamine (Gelsemium sempervirens "Margarita") here in zone 6 and it's perfectly hardy. Grows very well, but has thin stems so it's easy to control. What I really like about it is that it's evergreen, which is nice in our cold winters, and it is covered with really nice golden yellow flowers in spring. But it has to be the "Margarita" variety of Gelsemium to be hardy in at least zone 6.

Thanks for your response! I am in the Chicago area which I believe is zone 5. It sounds very pretty though!

Here Gelsemium sempervirens "Margarita" just limps along. Though it hasn't died, it gets killed back to the ground every winter and doesn't flower, so wouldn't probably get large enough for you.

Will you be providing some kind of structure for it to climb? All vines that I know of either need a trellis of some kind or they will cling to a surface. Is it just ivy they don't want or is it any vine that will cling to the brick? Other clingers that are less aggressive and more ornamental than ivy include Virginia creeper and the various climbing hydrangeas, including some that have lightly variegated foliage. IME neither will damage brick. I have both growing on my property so they will be fully hardy for you, but don't have either growing on a building. One type of Hydrangea is H. petiolaris (AKA Hydrangea anomala subsp. petiolaris, the correct name) and I have one growing on a concrete retaining wall that's probably 10 years old, and a young variegated form is just starting up a large tree trunk. Most vining Hydrangeas have white hydrangea flowers, though there is one selection with very pale pink, but I think that's in the genus Schizophragma, and it's not quite as hardy if I am remembering correctly. They all take a bit of patience to get going but can get to 40 feet if they have something that tall to climb.

If you want to battle a fearsomely thorny climbing rose, New Dawn gets quite large, but will need to be pruned and fastened to a trellis with clips or ties while you wear hand, arm, and eye protection. You may be able to find photos of the trellises used on the roofs of cottages on Martha's Vineyard. In winters like the last couple in the midwest (my mom had -11 in Cleveland, about a mile from L. Erie) any climbing rose will die back to the snow line IME.

Clematis need something with a diameter of less than 1/2" to climb, so if you can give it a trellis that fits that requirement and also fasten something up onto the roof for it to cling to once it gets than high, one of the larger ones might work. There are a number that get to 3-7 meters high that are hardy enough here such as C. summer snow Paul Farges. You can use the search function at Clematis on the Web - just put in the height range you want in the drop-down menu and leave everything else blank, and see what pops up. Not all will be hardy enough for you (such as C. montana varieties) but some will be.

In the Chicago area, the latest USDA hardiness zone map shows the metro area as zone 6a. I think if the wall is facing south or southeast, and with the urban heat island of the city, you might be OK with the Gelsemium "Margarita". It's fairly easy to find plants to buy online, and not really expensive, so it might be worth a try. Good luck.