I'd like to use the phrase: "Let's buy it at IKEA!" I'm not sure if I should use "at" or "in" in that particular case. Maybe both work? Is there any difference between them?
English speakers say they are at the store. If they are inside the building, they may say they are in the store (but they are also at the store).
"At" is used for location, while "in" is (generally) used to indicate being inside something.
Q: Where did you buy your desk?
A: At Macy's. It's sold in the furniture department, on the third floor.
Q: (on the phone) Where are you? I can't see you in the parking lot. Are you at the front of the store?
A: I'm in the store, over by the electronics section.
Q: (texting) Where are you?
A: I had to get out of the house, so I'm in the park. I'm going by the coffee shop, and will be at your house in an hour.
Unfortunately there are many idiomatic usages. For example, you may be in a meeting, at (or on) the computer, in deep contemplation, at a loss, and many others.
at is usually used for a location (IKEA is a location)
in, if used with a location can mean inside the location/space (IKEA is also a building, with an interior space).
I would have a preference for "at" in your example, however I wouldn't necessarily say that "in" before a location is wrong. It might be OK depending on context, for example if you were already inside the building when you said it.
Also, it's quite possible to say things such as "I'll see you in IKEA", or "I was in the bank when the robbery happened", when you mean inside the building.