I think you should first do this, and I DID do this, so dont' write it off as impossible, I did it for 5 months. (if seeing all of Europe is also /has been a dream, etc).........put all your things in storage. And rent out your house for either 6 months or a year. Have your car parked and only parked insurance so it's legal as well. (no bills except rental while you are away).
Then go to Europe. Stay in hostels and look up couchsurfing. There is a international youth hostels association that in many places the majority of people staying at them were older ones. But hostels are very cheap, you can cook your own food, and couch surfing network has people of all ages participating where you can find people who are happy to let you stay in guest room/couch/etc.
As for how to get around Europe, you can buy trainpass that for up to 3 months (buy it again if you wanted) but that lets you use all the trains and gets you all over Europe. (you do have to pay a reservation fee which varies depending on the train for a seat, some you can walk on and some a reservation is required). Public transportation is incredible in Europe, once you train into the city, they have subways, trams, buses, etc. You can also rent a car or if staying 6 months to a year, maybe buy one to then resell it. They also have discount airlines, easyjet,ryanair, which let you book up to 6 months advance and if you do book in advance you can get flights all across Europe and into Turkey, Egypt, Israel, etc, sometimes as low as $25 each way. (not including luggage).
Anyway how much it all will cost will depend on you. You can do it costing as much or less than staying at home. (if you pay a mortgage or rent payment). If you cook in hostels, etc, the normal 'cost of living' can be almost equal. The eastern european countries are very cheap. The ones that will drain you are Denmark, Norway, Switzerland, maybe UK. (they all have their own currency vs the Euro and tend to not get as much for your dollar). Egypt is DIRT CHEAP, but many would probably be uncomfortable right now. Turkey is really cheap too and incredible.
Anyway I'd do that first. Then if you do the USA part, I'd try to rent out the house. If you own it and no payments then get a cheap RV or finance one and have payments from house rental cover it and give you extra. Let the house keep going up in value and collecting rents. If you can't do RV anymore you can return to house or use rental payments to supplement staying in a nicer assisted living facility, etc. (Hmm, I should be a travel agent and a financial planner lol)