I have a question!

I'm a little confused about prepositions at and in but only when I'm talking about specific places for example:
I stayed at a Hotel but I can say I stayed in a hotel. It seems they both are correct, my question is: Why?

English has many different ways to say things, like a lot of languages, but here is the general concept:

at/in - "at" usually refers to a point in time, or a specific place

  "I stayed at the Hotel" - is a specific single place, easy to find (if there was more to this conversation)

  "I stayed at New York" - while this is a specific place there are two many parts to this place so you cannot say it this way.  "I stayed IN New York" - New York is a big place so you need to be more specific "I stayed IN New York AT the Holiday Inn hotel downtown IN room 223."

on - usually refers to being connected to something

  "Let's talk ON the phone"  - You cannot talk IN the phone (you are too big :)), you cannot talk AT the phone if you were trying to talk with someone on the other end.  You can talk AT the phone if you want to yell at the phone, but I doubt it would do any good.

  "The cat was ON the TV" - Now this could mean the cat was on a TV Show that you were watching or the cat was on top of the TV (in this case the word "top" is implied and you have to figure it out based on the conversation).

and/but - use these to join or separate an idea

  "The meal was great AND so was the dessert." - joining them together

  "Will you pay for both the shirt AND pants?" - joining

  "The meal was great BUT the dessert was terrible" - separating the two thoughts

  "The shirts is mine BUT the pants are his so he is going to pay for them." - separation

I hope this helps.