I often store old files I don't need anymore in a folder in Google Drive. This is convenient as they are out of the way and not using space on my SSD yet still accessible if needed. I'm starting to get into Dropbox. Can Dropbox be used in the same way as Google Drive or must a local copy always be stored in the Dropbox folder?
Let me rephrase this for you:
I often "upload" old files I don't need anymore in a folder in Google Drive.
You can do the same with Dropbox. You can upload files to Dropbox as well. The local files that take up space and are actually present in your computer are the ones in your synched folders. Meaning that you have them stored locally and in Dropbox in the cloud as well.
You can sync folders through your account settings:
Once there you can choose which folders to sync:
When a folder is unsynced it will be deleted from local storage but remain saved in the cloud. The benefit of that is that you do not have to wait for them to download when you want to access them from your computer.
Since you talk about old files I would suggest you upload them in the cloud (just as you do with Google Drive) and do not put them in a synced folder.
The ones already in your synced folder can be easily un-synced by just moving them to an un-synced folder in the cloud. Future files you can drop them locally in your synced folder and once they are synced (uploaded in the cloud), move them to an un-synced (cloud) folder as well.
PS: The screenshots are from a Mac.