Aleve, Aspirin & Ibuprofen are all from the same class of drugs called NSAIDS and all should be avoided for the week preceeding surgery.
You can take them after you are healed from surgery without problem - I have to take anti-inflammatories for my back problem.
Tylenol is always OK as is Vicodin (tylenol with opiates) - it won't thin the blood and can be prescribed by a doctor for stronger pain relief. Anything in the shape of a capsule, a liquid, or a pill (coated is better) smaller than an advil is OK but take with 8oz of water to make sure it passes through the band.
It used to be thought that NSAIDS could cause problems for banded patients, but that research has proved to be inaccurate. NSAIDS pose the same health risks for banded and unbanded patients, that is an increased risk of stomach ulcers or bleeding if you are prone to that problem. They can also cause stomach upset if taken on an empty stomach. I usually take them just prior to eating with a glass of milk, that's just what works for me