More realistically, a bathroom shower; the water plus the echoes from the tile/glass in typical bathrooms are better white noise than any digital solution. Two pots boiling at different heats also works and you potentially get the benefit of nutritious meal. Many kitchens also have noisy extractor fans conveniently located right above the stove!
Working in film, you want sound to be realistic but viewers have to be able to link it to something on the screen. Those loud hums from store/restaurant refrigerators used to be the bane of my life because while they were often the authentic natural sounds of the environment they're rarely visible unless you are specifically shooting a scene in a meat locker or next to an airport.
If I was shooting a remake of The Conversation for the digital age and my secretive chatters weren't using high tech wizardry, I'd give them two am radios tuned to bible or foreign language channels. 3 overlapping sound sources recorded at a single point (without the direction resolution our ears provide) are possible to disentangle, but it's a ton of work. Speech is harder to filter than music.
If you're in real fear of aggressive surveillance but must communicate, pick the noisiest room (usually the kitchen), sit on the floor or under a table, and hold your conversation inside a large cardboard box with some thick blankets over the top. I would sometimes use this when I needed to record in a noisy environment where it wasn't practical to run wires.