If you're on Windows, it's going to be in AppData > Local > Payday 2.
AppData is a hidden folder in your user's directory. You can find it by going to C:\Users<<steamuser>>\AppData\Local\PAYDAY 2\saves or by typing "%appdata%" in the location bar.
For Linux/Wine, it's going to be in the same location in the game's compdata data folder.
This is technically the backup save location if you want more information there's a steam guide for it here.

Just copy the saves folder to a safe place and you good!

Also some bigger rebalance mods like Eclipse will work on a separate save file and matchmaking from the main game already. Don't be alarmed if you see a default Dallas on them.
For less game changing mods like ReAi/FFS or stat tweaks these won't affect the save file at all so you're fine with these.