Your school has no sport facilities. Write to a nearby club to apply for membership.

Dear Sir/Madam.,
I am writing with regard to ask you some information about your services provided.

I am writing to ask about the services provided by your club. [1, 2, 3, 4]

I am a college student in New York Normal University and there is no sports facility in my campus. As I will stay here in the next three years, I need to find a place to work out regularly. I read your advertisement yesterday and I am interested in your services.

My favourite sport is swimming, so my first question is whether you have an indoor or outdoor swimming pool. Besides, it will be better if I would also like to ask whether you have tennis courts because I play tennis twice a week. Furthermore, if you have a golf club, please let me know.

At last Finally, I would like to know the annual fee of for the different levels of membership and please send me that in the reply.

Look I look forward to hearing from you.

Yours sincerely,  
Frank Yuan

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[1] I have noticed that you start most letters with "I am writing with regard". This is a very polite start, however you must follow immediately with what you are writing about.  For example:

"I am writing with regard to accommodation in your hotel."

"I am writing with regard to the sale of your car."

Here are two different introductions:

"I am writing to request information about accommodation in your hotel."

"I am writing to ask about the sale of your car."

Each of the above introductions is fine.  However, you should not combine these two different styles of introduction.  For example, the following introductions are wrong:

"I am writing with regard to request information about accommodation in your hotel."

"I am writing with regard to ask about the sale of your car."

[2] The phrase "to ask you some information" is not correct.  Either of these phrases would be correct:

"to ask you some questions"

"to ask you for some information"

[3] The phrase "your services provided" is not correct.  The word "provided" is working as an adjective of the noun "services", so this phrase has the same structure as "your apple red".  Any of these phrases is correct:

"your provided services" 

"the services you provide"

"the services provided by your _____"

[4] In the introduction of a formal letter, we often use "enquire" in place of "ask".  Here is the informal introduction:

"I am writing to ask about the services provided by your club."

Here is the formal introduction:

"I am writing to enquire about the services provided by your club."

Either introduction is fine.  However, some of your letters are quite formal, so this would be an appropriate word to use in the introduction.  Later in the same letter you'd simply use "ask".  The word "enquire" is rather formal, and we'd normally use it only in the introduction.