That's a nice question. The two are pretty similar, in that they describe an unoccupied location, but they are not quite the same.
When we say a place is "secluded," we mean that that place is not often occupied because it is "out of the way," or hard to get to, or sometimes just not well-known. I don't think peace or danger has anything to do with it. For example, when you hear about crime stories, you often hear that the murderer hid the evidence in a secluded location. But from a tourism perspective, where many tourists don't want to be surrounded by other tourists, finding a secluded spot is a positive.
When we say that a place is "deserted," we literally mean that the place used to be occupied, but that it no longer is occupied. A synonym for this literal meaning is "abandoned." However, "deserted" can sometimes be used metaphorically to mean that there aren't very many people somewhere. In this case it is a synonym for "unoccupied" and need not be negative. From a tourism perspective, it could be negative or positive, but is usually negative. For example, "we were excited to go to the state fair, but when we got there, it was deserted"-- this suggests there was nobody there and it was no fun.
A tourist agency may emphasize that a beach is secluded to tell you that it will be a nice place to go. In this case, "secluded" will be used more often than deserted, because deserted implies that people are leaving the beach for some reason, and the tourist agency might not want you to ask why! But again "deserted" doesn't have to be negative here, and I can see a tourist agency using either to describe a beach.
run away or flee sounds like something that refugees do: it's not something that you would want to associate with a paradise resort.
escape is probably a good word to use about the daily routine. It suggests freedom, which is a positive idea. get away is similar.
There is a significant difference between get away and run away, as explained here
I would recommend using escape for the first clause, then something different, also with positive connotations, in the second clause.
escape from daily routine and visit/come to/find sanctuary in our paradise resort.
Best Answer
Both verbs make sense in your context, but they mean slightly different things.
Getting away implies success: like FumbleFingers said, the movie probably ends with the character still on the lam. It also implies, albeit to a lesser extent, that the cops initially had custody of the character, which he escaped.
Running away does not imply success. I don't know if I'd go so far as to say it implies failure, mind you, but I wouldn't be as hopeful about the eventual fate of a character who was running away as I would be about one who was getting away. Running away also does not imply escape: he could have started off in police custody, or he could have started off free as a bird, we don't know which.
In other contexts, these verbs may or may not be interchangeable. For example, teenagers run away from home to get away from an abusive parent, but not the other way around.