The simplest method to get into a room is to wait for it to be cleaned, and once the door is open, simply walk in and take whatever you want. The maids will not ask you for ID. If you want to make it seem extra plausible, wave a similar hotel key at them as if you would have used it to open the door.

As for getting a replacement key, yeah, that usually does require some work. In lieu of asking for a replacement you can call the front desk on your cellphone and tell them you're standing outside your room and can't get to your key, and can someone come unlock the door for you.