I'm also a US citizen (and dual nationality European) who left the USA a few years ago.
Now I live in Galicia. Never regretted it.
The cost of living is a third of the one in the USA and in Galicia most people leave you alone instead of meddling, something that has changed a lot in the USA.
You can usually get easily allowed in if you are retired or have outside the country income in some other way, which needs to be proven. A health insurance is also mandatory if you want to stay beyond the 3 months as a tourist.
Spanish immigration is not as anal as US immigration and they often like Americans. You're not considered an invader.
Make sure NOT to close your US bank accounts but keep them on and also credit cards. They can be useful for out of country purchases and also for use here in country, since local cards and banks often put holds of up to weeks on on car and accommodation rentals while US issuers only allow holds of 5 days. The three weeks can be very annoying, as the holds are often large, more than we are used to.
Renting a large complete single family home with garden and beautiful views of mountains or sea will set you back a ridiculous $ 400 to $650 a month. Food is dirt cheap and very fresh and much more tasteful than in the USA. In small towns people in Galicia are kind, chatty and helpful without being too nosy. There are quite a number of Americas here, but they keep their presence unnoticed. It is very private here.
If you look for a job in Spain, I'm sorry to say you came to the wrong place. There is an enormous unemployment here. There is also a huge black market of services.
Health care insurance is also ridiculously cheap ($55 to $110 a month depending on age, of course no preexisting conditions). It allows one to access private providers here which are often excellent.
Otherwise there is the underfunded state health care which can only be accessed as an employee or an independent contractor. The latter pays about $275 a month.
Spanish skills are indispensable, so do not wait till you are here. Otherwise you will get charged more, will have bad business deals, bad terms, even some people who do not want to deal with foreigners. Very few here speak English.
If you have a pension or retirement benefit keep it paying out in the USA. Do not transfer it here. It is easier and cheaper to occasionally transfer money through Transferwise or Paypal and use ATM withdrawals.
Also do not open a bank account with a major bank but with a small or midsized one for starters. They will not scrutinize your US passport, which is a pariah passport due to the IRS FATCA law. Small and midsized banks have no US presence so run no risk. They are also often more customer friendly.
Also establish a mail forwarding account with a real US address before leaving (you need to show proof of US residence now due to new postal US law). Once you have it, it doe snot get checked again. It may cost $10-15 a month but is worth it.
Take into account that eventually you will need to report your income here and Spain now has a law that above 50,000 in assets your income gets taxed worldwide. So if you own more than that, this is a tricky place to be, unless you can put what you own in a trust abroad like in Panama.
Also take into account that packages often get lost/stolen or heavily taxed by default (even private stuff) in Spain. So get another forwarding address in a different European country and have packages mailed through that one.
The weather is often superb. In Galicia it never snows on the coast. The average temperature is 14 degrees but for at least 6-7 months in the year it is above 20 degrees Celsius, in the summer months even around 25-30.
Here in Galicia there is virtually no rush hour traffic. Highways are deserted when compared to US highways.
All in all it is still worth it by far! More freedom, lower costs.
Oh, and if you are looking for fixer uppers as a civil engineer) to create your own home, they abound here in such houses for as little as $10,000 and many below $40,000. Just make sure you do the bulk of the work yourself. And regardless of what you buy, make sure to establish that ownership is indeed with the seller. Many Spaniards sell properties that later turn out not to b fully owned by them.
Also get a 'gestor' sort of a CPA/personal representative, who can open lots of doors and protects you against the local tax man and other authorities. They are worth the little monthly subscription fee of about $70.