Which material to use for athletic accessories?
For plastics, my first instinct for the first two properties would be a polycarbonate plastic. Polycarbonates are known to be very strong plastics (tensile strength up to ~70 MPa) and deform without breaking under many conditions, which is why they're commonly used in things like safety glasses and bullet-resistant glass. It also looks very interesting as it's quite optically clear. PC is 3D printable, I've seen a few people using it in hobby printers (http://www.protoparadigm.com/blog/2011/12/printing-polycarbonate/) and in very high end StrataSys printers, but it's not a super common material so it might take some experimenting.

Another option is a nylon. There are a number of different types available and many have similar properties to polycarbonates (minus the optical clarity). Nylons seem to be a bit more popular for 3D printing and I've heard good things about the Taulman filaments.

Of course, you're not limited to a single material and there are many things that could potentially be used in this kind of application. Often, the combination of multiple materials makes sense (e.g. a metal insert in a plastic part).

Something like carbon fibre-reinforced epoxy construction might be appropriate. It's not 3D printable, but can be constructed in layers around a lightweight (expanded polystyrene or the like) form. This approach is often used for parts that need to be very light while having high tensile strength (think bicycle frames, ski poles, etc.) I could see a carbon fibre-wrapped plastic insert making a very strong and light shoe heel.

Ultimately, these things are balancing games between strength, mass, fabrication cost, aesthetics, etc. but these are a few potential materials that come to mind.