Answer: You need a vine that can cling to the concrete surface. Unfortunately, honeysuckle is a twining vine, and it won't have anything to twine around. Ivies can cling, but they don't like to climb hot masonry walls. It might do fine in a partially shaded spot. Virginia creeper might be a better choice (Parthenocissus quinquefolia). It seems to withstand and thrive in most environments, and has excellent ability to cling to masonry. It also turns a brilliant red in the fall. Silver Lace Vine (Polygonum auberti) is another possibility; it has sprays of white flowers and is a vigorous grower. Perhaps a combination of vines will fill all your wishes!
By the way, clinging vines can cause damage to masonry over a long period of time.
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