I feel I have a decent understanding of both of those particles, but I'm wondering how the meaning of the sentence changes with and without the は after へ.
は is the topic particle and can be used in combination with a variety of particles. When combined with the subject particle が or the object particle を, は usually replaces が or を. With all other particles, it goes after the particle. (In fact, を＋は may also turn into をば, see Dono's comment.) In your example sentence, it makes ゴルフ大会へ "to the golf tournament" the topic of the sentence.
A similar sentence would be
and the difference between this and your sentence is just the difference between に and へ.
One definition of は is as the "topic marker particle." In some instances, you can better understand the meaning by (clumsily) translating it as "as for." So in this instance one could translate the sentence as follows:
Which would be translated in "natural" English as:
In spoken conversation, one could expect to hear this sentence without the は, as follows:
This would be less formal, and one could even drop the へ to make it more casual:
So the first example would be the most grammatically correct, as well as the most polite and formal.