It probably would be a good idea to let us know what camera you are using. It probably doesn't matter too much, but then again depending on the model you may have some other options.
Let us know as well are you using Windows or Mac?
In most circumstances you won't be able to directly connect the camera to a card reader and accomplish anything. You might be able to accomplish some direct transfers with a tablet, again depending on what you have.
If you are staying in hotels that have a business center, you could have a large SD card, say a 128 GB, and move the contents of a 16 GB card to that 128 GB card, in theory 8 times using the business center computer. That is a simple copy, paste from the small card to the big card. That makes the assumption that the 16 GB is near full each time. That might be an unlikely scenario, depending on whether you shot RAW, JPG, or both (do you know). Once the small card has had its contents moved, I would suggest an in-camera low level format of the card.