Dixie,
I have been retired for 5 years on a small pension. I don't live off of the grid, but I can give you some very helpful advice.
1. Take your pension payments over time, not in lump sum. If you take a lump sum, it will be lesser than the lifetime of payments that you will end up with by taking it over time. Also, how would you invest your lump sum? You can only get a 2% return on long term CDs right now, and that is taxable! Unless you absolutely need the money in lump to acquire your future home, don't do it.
2. Anytime that anyone says that they have a dream of custom building a special kind of house, it ALWAYS ends up being a money-sucking disaster. It always takes twice as long and twice as much money as they estimated. And the results are generally poor. Wherever you end up living, how many experts will live around there who have built quality underground houses? Probably none. Some "contractor" will fumble through the job, and it will end up leaking. Money is too hard to come by to use it to pursue an amorphous dream.
3. It would be 100% bettter for you to find a small old existing one-story house, with a nice clean dry basement, hopefully that has a few windows above ground to let sunlight into the basement. It can be old and well used, but not abused. No rot or termites. And must have a good roof. Then, spend your money doing the following: (i) insulate the heck out of the upper floors, (ii) install one or two large woodburning stoves upstairs that vent to the chimney, (iii) install one large woodburning stove in the basement that vents to the outside, and (iv) vinyl-side the exterior of the house. After doing this, you will have virtually no maintenance expense keeping up the exterior (painting, scrapping etc.), and you can live like our great grandparents did. You will spend the summer living in the basement, and the winter living on the floor level.
4 As far as picking a state, the most important thing of all is that you end up in a state that you really like, and that has moderate winter and summer temperatures. This means the border state regions (Southern Missouri, Southern Kentucky, Eastern Kansas, Northern Arkansas, Northern Tennessee, perhaps northwestern Virginia or northeastern West Virginia). All of these areas have a low population density, wonderful hunting, lots of hardwood forests, and lots of public land to hunt. They also rank as among the cheapest areas to live in the U.S. Research these areas, and find the cheapest. By the way, Tennessee has no state income tax on wages, but does tax interest and dividends.
5. Every place you will ever go will have property taxes. These taxes are, in most places, assessed by the county, and how high the tax rate is set is dependent on local politics, and on how many services people demand. Rural areas, with few people and few roads, have low tax rates. Here is some crucial information: In almost every county I have ever lived in, there is a special very very low tax rate (called the Agricultural exemption), if your land is used primarily for agriculture (production of hay, grain, crops, livestock, etc.). Most require 10 or 20 acres as a minium. All you have to do is find a place with 20 acres of old fields, find a farmer who wants to cut and bale it twice a years for hay, make a sharecrop agreement with him by which he keeps 90% or so of the proceeds, fill out a one page form with the county listing the crop, your name, the property location, the estimated yield, and the farmer's name and address, and you will qualify for the special tax rate! It is shockingly low. (I own 12.5 acres in Hanover County, just 45 minutes west of Richmond, VA, and my total real estate taxes are about $55 a year. That's right. Fifty- Five dollars!
6. About 100 years ago, the vast majority of Americans lived comfortably off the grid, without electricity. They didn't do it by moving to Alaska or building underground houses. They did it by living on small self-sufficient farms with woods and pastures, having good gardens, raising a dozen pigs or feeder calves, and taking a few deer each year. They never bought what they could rent, and they never rented what they could borrow from a neighbor.
Hope this info helps. You don't want to end up choosing a place solely on its low cost, and end up in with an inferno summer, or a 6 month winter. You will be living in hell and get extremely depressed. The main point is that you want to enjoy your retirement.
Regards, Mannyrock