Where is the memory inside this RFID tag

Won't help - RFID tags all have a unique number on them. And when I say unique I mean 64 bits unique, maybe more. This is 'more atoms than the universe has' unique. They keep a list of the people who are allowed to use the elevator and know what numbers they have. So if your tag hasn't been entered into the system you can't use it. Unless you could get your hands on one of the 'masters' tags and copy the number. But if you can do that just use that tag. Theft, sure, but you're already asking how to elegantly trespass so I'd assume you're okay with theft?

No, they're not globally unique, they're unique per manufacturer. For one thing, not all manufacturers use the same code length. If I want to start producing RFID tags tomorrow I can do whatever I please to do, like producing two RFIDs for every code, or even produce a whole batch with the same code. If you want to have them unique, you'll have to stick to one manufacturer.
That said, the codes are pretty long, so chances are slim that you'll have two colliding codes.

In the (near?) future RFIDs are going to replace bar codes in logistics. Those will have a combination of a non-unique product code, like EPC (European Product Code) and a unique ID.