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You cannot "live" in Germany - that by definition requires a residence permit.

So, unless you get a Family reunion Visa through your wife, I assume you want to come for an extended tourist visit - you are allowed up to three months in the Schengen area in any rolling six months period.

German landlords are usually unwilling to rent their (generally unfurnished) flats to short-term foreigners, so you might have to stay in hotels or other short-term places.

A car is not necessary (and in my opinion not advisable), as good and reasonably priced public transport is available everywhere.

Get a travel health insurance that covers the long durantion of the trip (many do not!).

As Beppi mentioned one can stay up to 90 out of 180 days as a tourist, and for US citizens this is without visa. Even being married to a German doesn’t help one to stay longer unless they actually move to Germany say with a family reunion visa and establish residency. But this is complex if not impossible if one is coming and going and not spending most of their time in Germany – and fulfilling the requirements one needs as a resident. For one, travel insurance will no longer be a real option, one needs to get insured on the German system as a resident.

As a German citizen, the wife would have it easier to rent a place but if for short times then one is usually going to look for more of a AirBnb set up.

Owning a car in Germany when one is only occasionally then is not wise if even possible. One has to have residency to register and insure it. There is plenty of public transportation or car rentals.

@rodnbarb

As has already been said, you´d be restricted by Schengen visa rules, so, if your plan is to stay in Germany/Schengen for three months, then return to the US without any plans to immediately return to visit one or more Schengen countries again, this would work for you.

There is the possibility to temporarily import a vehicle for up to six months, which may be less expensive than renting a car for a solid three months period. Personally, I´d not do that.

There is also some sort of short term lease program for non-EU tourists by French car makers (Citroen and Peugeot maybe?) but I don´t know much about their T&Cs.

If you don´t have mobility issues, I´d get a Deutschlandticket - 49 € per month per person covering all regional public transport only excluding express (IC/ICE) trains. You could rent a car for a day or two every now and then to visit areas that really are inconvenient to reach otherwise.

You´d need to rent a vacation rental (furnished, utilities included, etc.) , which will be easier/cheaper during shoulder and off season.

What´s the plan? Staying in one spot for three months to be close to family or seeing different areas for a few weeks or a month at a time?