What are some arguments against Hedonism?

That overall life satisfaction is very important and isn't necessarily acquired through just experiencing moment-to-moment pleasures. Although I suppose it might be possible.

Epicurus would agree with you, and he would call your position hedonism.

There are a variety of arguments against hedonism, but they tend to be directed towards a particular version of hedonism. While hedonism is generally an identification of the good with pleasure, most hedonistic theories tend to further qualify the assumption. For example, Epicurean hedonism, aestheticism, and (to a some degree) Utilitarianism are all hedonistic theories; but one cannot be reduced to another, nor is each counter-argument effective regarding all. Do you have a specific type of hedonism in mind?

The only things that come to mind right now (granted it's late and I'm tired) are someone's personal religious beliefs (all major religions I'm aware of hold abstinence and self control in high regard) and the common sense that should tell you that a life spent chasing pleasure just isn't bound to be healthy in the long run.

One important question (if you are going to discuss arguments either for or against, hedonism) is to say what hedonism is). Generally, it is the view that pleasure is the summum bonum, the ultimate standard by which the value of all other things are are valued. A question that rises right away is whether hedonism is the view that all pleasure is good, that only pleasure is good, or that all and only pleasure is good? And depending on what hedonism is taken to be, the arguments will vary. (1) Is all pleasure good? But are there no such things as evil or bad pleasures? For instance, the pleasure that Germans call "schadenfreude" which is the pleasure a person may take when he sees another person in distress. Maybe a person he dislikes. Is that pleasure good? (2) Is only pleasure good? Are there really no other good things besides pleasure? What about helping others in distress? One need not take any pleasure in doing so, but would that mean that helping others is not a good thing even if it is not pleasurable?

So, in order to discuss hedonism intelligently, you first have to try to understand what hedonism is, and then, depending on that, construct your arguments.