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My incredible trip

Last week I went to Asturias for a few days.
I stayed in a spacious and comfortable residence, which was located in Oviedo.
The room was inexpensive,; we just paid paid just ["just paid" refers to the exact moment that you paid. "paid just" is the same as "paid only" and refers to the cost of the room] 50 € for four days.
The first day, we visited the Jurassic Museum, which was located in Colunga.
The Museum offered a guided tour of the several species of dinosaur in its galleries.
After that, we ate at a typical restaurant which served tasted tasty food.
We were pleasantly surprised by the cheapness low-cost [cheapness doesn't work; other options are: "low-cost" or "...by how cheap the bill was."] of the bill. In fact, we just paid one menu instead of paying two. [I don't understand what you are trying to say. Perhaps this: "In fact, we had to pay for only one meal, instead of two."]
In the afternoon, we went to the Ribadesella' s Port.
The next day we went up to the Covadonga's Lakes. There were animals in the middle of the road. The landscape was an amazing sight, so we profited ['profited' doesn't work here; perhaps you are thinking of 'take advantage'] to take lots of photographs. [try this: "...amazing sight, so we took advantage of the opportunity and took lots of photographs.]
When we went down to the montains we went to the Restaurant and we didn't stop eating until we were full.
Unfortunately, I felt sickness sick and I disguised regretted [I don't understand what you are trying to say] everything that I have had eaten.
My sickness soon passed and I felt better.
After lunch, we visited a friend, who lives in Llanes and we spent the afternoon with her.
On Saturday morning we walked for to Oviedo for a while despite of the bad weather
When the rain finished we went to Gijón and we were went strolling along the beach.
In the afternoon we went to Cudillero, it's a touristic touristy [touristic is correct, but it is a little out-dated. 'touristy' is a better word, but VERY informal] place, where people fishing fish during their working life work.
The next day I felt depressed because I didn't want to come back home. ["return home" sounds better than "come back home"

¡Espero que mis correciónes estan muy útil! ¡Suerte!