Bikers aren't exactly known for looking elegant. In fact, they're usually considered to look pretty gruff, rough, and tough. While it's possible to wear a leather jacket and leather pants and somehow make it work, it's not exactly something you'd wear to a formal event. Is it possible to ever make your patch-covered jacket look nice and elegant? Well, it depends on what the occasion is.
Your biker gear will never really look right at a wedding unless, of course, it's a biker's wedding and everyone is wearing their riding gear. Such events do happen, bikers who marry other bikers often incorporate their love of motorcycles into their ceremony. Some even get married on their bikes. But for a regular wedding or other formal ceremony, you'll probably want to leave your biker jacket behind. However, you could slip a small patch onto the front of your more formal jacket if it's one that isn't too crass or colorful. A small pink ribbon patch, for example, could be worn in honor of those who have battled breast cancer.
Another option is a veteran's patch. Some of these patches were designed to mimic the ribbons and awards given by the military. If you received a purple heart, for example, there is a patch that closely resembles the actual award. Some servicemen wear these patches on their civilian clothing in place of the actual ribbons, which should only be worn on their military dress uniforms. One or two of these patches may also be excused when worn to an event that requires dressing up. Just don't go overboard with it.
There are some patches that do look elegant, but most of them are special, such as these examples where the patch is showing support for a cause or is a military honor. Use your best judgment when deciding whether a patch is appropriate for the event or not.