We can come over and stay for 6 months as visitors without a visa since we are U.S. citizens and then go back to the U.S.
Just as a heads up and to clarify, you
do need a visa to visit the UK. US citizens have the benefit of not being required to apply for entry clearance
in advance of flying to the UK, but when you land and have the interview with the IO, that IO is deciding on the spot whether to grant you a visitor visa or not (which will be the stamp in your passport).
Six months is the maximum permitted time; the IO may decide to grant 3 months, 1 month, 2 weeks, or not allow entry at all. Please take care and do not equate the benefit of not needing to apply for a visa in advance as not needing a visa at all. Some Americans have gotten caught up with this as they were under the impression they were automatically entitled to a 6 month tourist stay and found out that wasn't the case, and it ended up being a rather costly mistake.
If you aren't sure you would have enough evidence to allow the IO to grant you a full 6 months upon arrival, you could apply for an advance visitor visa. That way, you would be sure you would have prior permission to stay for such a long amount of time and not take a gamble that you'll be at the mercy of the IO that day.
Another thing to consider when making your plans, would you be able to financially support yourselves during those 6 months without
any work while you're visiting?