Native speakers simply wouldn't normally say "I'll show you into to your room". The two credible possibilities are...
1: "I'll show you to your room"
Appropriate in contexts where the offer is to help you find your way to the room, or simply to act as a "protective escort". The speaker might reasonably leave as soon as you're within sight of the door.
2: "I'll show you your room"
Appropriate in contexts where the offer is to accompany you into the room, perhaps to point out anything that might not be obvious (where the light switches are, how to operate the minibar if it's a hotel room, etc.)
In practice, both contexts often apply simultaneously, and either of the above phrasings could be both intended and understood as implying the other.
For reasons that aren't immediately obvious to me, although I've said into is unlikely in OP's exact context (with a room), it seems perfectly normal to me to...
3: "Show him into the garden"
...which carries no particular implications of presenting the garden - just going with him to get there.
EDIT: In informal contexts such as a guest staying overnight at your house, #2 above (no preposition) is the normal form. In formal contexts (hotel staff, a wealthy person's house-servants, etc.) to is more common, carrying either/both implications of guiding and/or escorting.
The relative uncommon into (almost always formal) implies the speaker will accompany you through the entrance (door, gate, etc.) to wherever you're going, and assist you in "settling in". Thus, anyone showing you into the garden would usually accompany you into the garden and introduce you to your host and/or other guests. If a hotel manager shows you to the dining room, he might well just leave you at the doorway - but if he shows you into the room, he'll probably usher you to a table and see that you're seated before leaving you in the care of the restaurant staff.
Run away means you put distance between yourself and the unpleasant thing. It doesn't say whether your escape was successful. It doesn't say whether you're coming back. It doesn't say whether anyone will catch up with you.
Run off means you went somewhere that you cannot be effectively retrieved either because you went someplace hard to reach or because no one knows where you went. It usually implies that you're not coming back. "Run off" can almost always be changed to "run away" without making a statement false.
A specific use of "run away" is actually closer to the meaning of "run off", and that is when a child or teenager runs away from their parents for a long period of time (days, months, years or permanently). The child or teenager is said to be "running away from home" and is referred to as a "runaway".
http://www.merriam-webster.com/dictionary/run%20off gives another usage of "run off".
Run off can refer to causing someone else to run off.
- "I ran off the intruder by chasing him and throwing rocks at him".
- "The intruder ran off when I chased him and threw rocks at him".
Both sentence are good and mean pretty much the same thing.
Best Answer
The subtle difference lies. I'll try to explain 'have been' and 'went' irrespective of the answer stated there that might have confused you.
Have been is generally used to say you had gone to that place and come back. On the other hand, went in this context talks about your presence on that place in the past.
...means at least once I had gone to the states and come back.
Think about this - if your friend asks you, "Have you gone to America?" This would be unnatural to many. On the other hand, if he wants to ask whether, in your lifetime, you have ever visited America, the better construction is "Have you been to America (ever)?"
So, to answer this in the context of visiting the places, if you want to say that you had visited that place and had come back, the better way is have been and if you are more concerned about your presence in past, use went as in " When I went to New York City, I learned that Americans there are very amicable".