1. Always, always, always carry your race gear with you on the plane!
DO NOT, I repeat, DO NOT put your race clothes, shoes, and other gear in your checked bag. Sure, you may have never had a bag get lost by the airline, but do you really want the first time to have your shoes in it when traveling for a race? I didn't think so. If you are traveling for a longer period of time that will require a checked bag, I recommend checking the stuff that can easily be replaced like clothes for the vacation part of your trip and putting the critical items in a carry-on bag.
Yes, it sounds silly, but I have had friends go on a run the night before leaving for their trip and left their shoes at home or in a gym locker. My worst nightmare for sure. I was introduced to the Klitch Footwear Clip a few years ago and I love it. The Klitch is is shoe holder that can clip onto the outside of your gym/running bag, suitcase, etc. It is perfect for traveling and I always use mine on race-cations.
If running multiple races, I recommended laying out and packing your race stuff by race. For Disneyland Half Marathon weekend I am running 3 races so I pack for each race separately. I layout my shirts, shorts, skirts, socks, etc for each race and then use drawstring bags to travel with. This makes hotel life a lot easier as everything I need for the 5K on Friday is already together, so I just grab my bag and I am ready to rock!