I highly recommend the Secret Lagoon. We visited in the late morning when most folks there were local and it was not at all crowded. What was so amazing is that there is a geyser that goes off every so often right beside the soaking pool!! The locker rooms were very clean and comfortable.
Near Reykjavík I recommend the Sky Lagoon. If you select the “Pure” option, it is very reasonably priced. Its infinity pool is beautiful, overlooking the ocean. Great shower and locker rooms. The bar is carved out of rock and you wade to it— the bartender hands you your beverage without your having to leave the water.
The water is not super warm—a bonus for some people. You will need a reservation. They control the number of guests, which makes it a pleasant experience