If you don't believe in gods or some sort of higher power, and you don't want some mortal telling you how to spend your life, what do you do? What is your purpose? Whatever you want it to be.
If you want a driving purpose, you have to choose one - make one up. Most people are theists, so they have their supposed purpose shoved down their throats from an early age, i.e. "to serve God." But then they may spend years trying to figure out how to best serve their gods, so then end up at basically the same place as non-theists, without a definite direction or goal.
As a rationalist, you may want to use reason to derive your purpose, but even there, there will be personal decisions. You're going to have to lay down some axioms on which to build your reasoning. Just as you have to define what + and × mean in order to do math, you have to set down some subjective propositions so you can build up your philosophy. (The same goes for morality - if you want to base your moral code in reason, you still need basic propositions to build it on.) You can make general goals and extrapolate into specific, or you can just think about things that you want and figure out how best to achieve them. Hopefully an example will make the need for subjective propositions clear.
Picture Jen: a 29 year old atheist who has kids, a spouse, brothers and sisters, nieces, nephews, parents and friends. She cares deeply for her spouse, children, and family. She wants them to be happy even after she no-longer exists. Jen can build her axioms off of her deepest desires: to enjoy her life and to ensure a great future for her children and surviving loved ones once she is gone. Jen can build specific life goals from these desires, and achieving those goals becomes her purpose. To ensure a positive future for her children, Jen wants to make a positive contribution to the world while avoiding destructive behavior, and working to influence other people along the same lines. If Jen works for a living, she is going to want a profession that makes a positive contribution to society. Suppose Jen has a communications degree. She should avoid a career in marketing cheap, plastic crap, and try to work for an industry that provides a useful service or product. Otherwise, if Jen is a stay-at-home mom, she could contribute through volunteer work. And of course, she is going to want to be the best possible parent to her children.
Hopefully, it's clear that from a few general desires, Jen can make rational decision about how she should live her life in order to maximize the chances of fulfillment. Jen's purpose in life is to have a positive impact on her children and society through responsible parenting and work that she enjoys. What makes this purpose fulfilling is that it is already based in something that is deeply meaningful to Jen. To show that purpose depends on passion, let's look at passionless life.
Suppose Jane is a single, childless* atheist. She has a few friends and relatives, but she isn't close with any of them. When she looks at her fellow citizens, she sees people who are only kind when it is convenient, people who don't think about long-term consequences of their actions. She sees a society that is unsustainable, careening toward its own destruction. If Jane isn't emotionally invested in the rest of the world, then she isn't going to have much stake in the future beyond her life. Goals based in the long term future don't make sense. If Jane had some particularly compelling interests, she could build her goals around those interests, incorporating work if possible, but otherwise just working in such a way that she has enough free time to devote to her interests. Without compelling desires, Jane has little reason to work for her goals. Her purpose feels arbitrary and insignificant.
To make a meaningful and fulfilling subjective purpose built with logic and reason, one must build upon non-rational passions. To feel fulfillment, one must feel desire. If one does not have strong desires, one is unlikely to find meaningful purpose. That's one reason Vulcan society doesn't make sense to me. Once you've squelched all of your strongest desires, what is left to motivate you?
*I am not saying that you can only find fulfillment through marriage and children. Having children makes not caring about the future less likely, but not having children does not preclude developing strong emotional attachments or caring about the future.