Is the beach near my holiday resort?

plaja benim tatilyeri yakında mı?

--------------------------------------

You done good ! but little bit correction needed.

Plaj benim tatil yerime yakın mı ?    OR ;

Plaj benim tatil yerimin yakınında mı ?

--------------------------------------------------------------

tatil yeri --> two seperate words --> holiday place

[benim] tatil yerim --> my holiday place

tatil yerim + e [dative case] ---> to my holiday place

yakın mı ? ---> is [it] near ?

I have already been at the travel agency.

Ben seyahat acenteside zaten vardım

---------------------------------------------------------

Seyahat acentesine gitmiştim.

Seyahat acentesine gittim zaten. 

Daha önce seyahat acentesine gitmiştim.[gittim]

---------------------------------------------------------------------------

I´d like to go near the south coast.

Güney kıyısında yakındanın gitmek seviyorum

----------------------------------------------------------

Güney sahiline yakın bir yere gitmek istiyorum.

[Literally ;  I´d like to go somewhere near the south coast]

-e yakın = near to

-----------------------------------------------------------------

Ankara´ya yakın bir yere gitmek istiyorum. ---> I´d like to go [somewhere] near Ankara.

You are right, hocam, nasıl also used in place of neyle, but I think it will be useful for a learner if we explain the difference between these two question words.

If you are asking about the way to some place:

Oraya nasıl gidebilirim? ( lit. How can I go there? ) => can you tell me the way to there? What route should I take to get there?

"If you are asking about which transport you need to catch":

Oraya neyle gidebilirim? ( lit. By what can I go there? )

I´m not sure if your answer is correct or not.

Maybe it needs something more for "the" trip

Yolculuğu ne kadar?

Yolculuk (trip) + u (the) = yolculuğu (k mutates to ğ

Yolculuğun fiyatı ne kadar?

Yolculuğun fiyatı ne?

Seyahati ne kadar?

(I notice that seyahati does not follow normal vowel harmony rules) 

This previous post was also interesting to me.

Would any Turks like to comment if they agree with the differences about the Turkish words for ´trip´

Do you agree? 

Henry you cant make a word definite always with adding ı/i/u/ü suffix. Because verb also must allow the suffix.

Arabayı kim sürüyor? Who drives the car? (Here it is okay)

Yolculuğu ne kadar? This is wrong because u here can only be a possesive suffix. You need another noun here.

İstanbul yolculuğu ne kadar? How much is the İstanbul trip?

Yolculuğu yaptın mı? Did you do the trip? You see here it is definite because verb also allows it to be definite.

Teşekkürler Gokuyum 

The main thing to know here is you can not make a subject definite with adding ı/i/u/ü. If you add this sufix subject will either transform to an object or it will need another noun and the suffix will function  as it is a possesive suffix or it will not mean anything.

Thaks for all ,many thanks

çok teşekkürler Tunci