Okay, here goes.
I could probably (literally) write a book on why I think it's silly to be a nihilist and an atheist, so I'll limit myself to just a couple of the strongest reasons I reject that view.
Let's first define nihilism as a system that rejects all value. Let's define value as incorporating both concepts of *meaning,* and concepts of *utility.* Now to the analysis.
Before I make any actual arguments, I first want to express puzzlement at the implicit attitude that many theists seem to have about finite things. Many theists seem to express the notion that if something is finite, it is pointless, and argue that atheists should be nihilists because in an atheistic schema all things eventually end on a permanent basis (straw man given cyclic and multiverse models of the universe, but that's a tangent).
Experience, however, tells me that this reasoning is faulty. I have never heard a Christian argue that marriage is pointless just because in heaven the souls "neither marry nor are given in marriage" (Lk. 20:35). I have never seen a Muslim turn down a hike just because it won't go on forever. I have never seen a Jew stop composing just because his music will not be needed in Sh'ol, and so forth. In short, humans instinctively recognize the utility of now and do not demand eternal meaning or utility in order to find value in something finite. I have sympathies with Camus here.
Similarly, the basic error many theists (and most nihilists!) make when analyzing atheism is to suppose that if there is no UNIVERSAL value, that there can then be no LOCAL values (the fallacy of division). This is where I will fundamentally disagree. I don't have to prove that "The Lord of the Rings" is divinely inspired scripture in order to prove that it has meaning, *to me.* I don't have to prove that a new library in town will benefit the Andromeda galaxy in order to prove that it will benefit the citizens of the town.
All meaning is created by someone. A being does not have to be subordinate to a higher purpose in order to have his own meaning and purpose -- otherwise, theists are in trouble, 'cause there would then be no point to GOD'S existence! :P
I fully concede that it is possible to be a consistent atheist and a consistent nihilist. However, based on the above, I am also forced to concede that atheism does not ENTAIL nihilism; if I can consistently construct a coherent local meaning and purpose for myself, then I can consistently accept this meaning and purpose while remaining an atheist. It is perfectly possible to be, for example, a fictionalist, or a Platonist, while remaining an atheist.
So that answers the charge that all consistent atheist are nihilists. Now on to why I reject nihilism.
First, the burden of proof is ridiculously low. By definition, there can be no *reasons* supporting nihilism. Even if nihilism is true, there can be no reason to adopt it; nihilism rejects rationality and coherence. For example, if you value honesty such that it is dispositive in your decisionmaking, you are living according to an ethic of truth and are therefore no longer a nihilist. Nihilism is also definitionally *useless.* There can be no such thing as purposeful or useful nihilism; it ceases to be nihilism at that point.
Therefore, if there is ANY reason -- even just one -- to reject nihilism, OR any reason to adopt a non-nihilistic view, OR any view which has higher utility than nihilism, then it is rationally justified to reject nihilism.
So, first, the big reason to reject nihilism is that, well, it's nihilism. It ultimately consumes itself, as the ultimate form of selfishness. It doesn't give insight; it doesn't help the self or others; it doesn't make you happier; etc. And since with nihilism longer existence has no greater value than shorter existence, true nihilism tends to end in its most consistent manifestation: Suicide. Nietzsche recognized this, and said the only antidote to suicide would be to create your own meaning and purpose -- which is exactly what I've been saying.
My instinctive will to live and my instinctive desire for a worldview that adds something to my existence are, therefore, two very good reasons to reject nihilism -- and since nihilism runs directly counter to these impulses, actualizing these two fundamental aspects of my being is also a good reason to adopt a non-nihilistic framework.
In fact, human nature itself is a good reason to adopt a non-nihilistic framework. What sets us apart neurologically from other forms of life is our extraordinarily powerful ability to perceive meanings and connections in otherwise-isolated noise, or even within larger forms of order. (See, e.g., http://www.holycrossovers.com/wp-conten
This extraordinary pattern-seeking ability is an evolutionary adaptation that developed as a means to enhance the survivability of the human species. What this means, in short, is that humans are built as meaning-making machines (see esp. Dr. Michael Shermer's work on patternicity/agenticity). We crave meaning, and we crave certainty. As communitarian animals, we also have an intuitive moral sense, and we also have an instinctive drive toward pleasurable experiences. Neither of these human drives is fed or satisfactorily accounted for via nihilism.
Thus, any coherent affirmative system -- whether it constructs meaning, seeks happiness, or attempts to promote some definition of virtue -- is superior to nihilism, just from an intuitive human perspective. For starters, I would note emotivism, prescriptivism, utilitarianism, and even Kantian moral realism as moral systems which work quite well and quite consistently without any supernatural beings, serving thus as more attractive options to ethical nihilism. As to broader life philosophies, I would say that at LEAST postmodernism, secular humanism, Epicureanism, Cynicism, Kantianism, naturalistic pantheism, absurdism (with some reservations), social Darwinism (not that I endorse it at ALL), and even some forms of Buddhism, Platonism, and Stoicism are all available to the consistent atheist.
As to how my specific outlook differs... well, I'm broadly a humanist with strong leanings toward naturalistic pantheism (the two views do not inherently contradict). Hopefully I've given a few examples, but for a a look at how I live in a more positive and fleshed-out sense, you can go to my "Answers to Twenty Questions" note on Facebook or else talk with me directly via email/private message. Either way works. :-)