I am still a little stuck on when to use the object marker.

With Sevmek, when do we use it, always?

I know we should say seni seviyorum rather than sen seviyorum.

But what if we like a place or a food or music?

Is it this correct? Müziği seviyorum.

Yes, müziği seviyorum is correct. Whenever you use sevmek, the object takes accusative case endings.

I would prefer saying "Müzik dinlemeyi seviyorum". Sevmek always wants you to use this -i suffix with the object.I use object as a grammar term here. A person can be the object too. And  "listenning to music" is the object in my sentence. An object can consist of more than one words too. So we put this -i after "müzik dinleme". But two vowels can not come together in Turkish so we put a y between them.

müzik dinleme-y-i

Wow, interesting question. Normally we use object marker for definite nouns. But it seems there is an exception for sevmek because we always use object marker with it. I don´t know the exact reason but it doesn´t sound right when you don´t use it without object marker. 

If you want to talk about something general instead of specific you can make the noun plural like "bilgisayar oyunlarını seviyorum"

Sometimes people  drop object marker when they use “sevmek”  preferably in aorist form and it may still sounds ok. Especially with adjective phrases.

Ø + sever / seviyor  + personal suffix

Kahve sevmem ---> I don´t like coffee.

Sütlü kahve sevmem. --à I don’t like coffee with milk.

Sütlü kahve seviyorum -àI  like coffee with milk.

Eskiden sütlü kahve severdim. à I used to like coffee with milk.

Bahçede çok çiçek sevmem. -à I don’t like many flowers in the garden. [I don´t like having many flowers in the garden ]

Kuru kayısı severim. -à I like dry apricot[s].

Türk kahvesi sevmez -à He/She doesn’t like Turkish coffee.

* This object marker dropping is NOT applicable to all words or adjective phrase.

* We also come across this dropping with phrasal expressions , such as :

" Sevdi mi güzel sever " ----> When he loves, he loves the beautiful one [s] 

                                        [ He falls in love with only the beautiful ones ]