I'm so sorry for your loss. Please take care of yourself at this difficult time. I think your idea to challenge yourself is a good one.
Not knowing how old you are, what your budget is, where you live in WA or how close you are to medical facilities, I have concerns beyond the day to day practical ones like transportation, food shopping, cafes and restaurants. I'm 77, so I think about these things. Below are some questions and thoughts for your planning.
Since you'd like to rent the same place for a long time, I recommend that you start looking for apartments using Booking.com to get an idea of potential costs in the various locations you're considering.
When you do that, things to consider include the ones below as well as some I'm sure I've forgotten. I'm mentioning these things because I've rented many apartments when traveling in Europe, but the longest time has been 8 nights. If I was going to be in one location for 4-8 weeks, I'd be a lot pickier about what that place is like. I've rented apartments that were not as advertised and/or pictured. Airbnb and VRBO were the worst about that in my experience.
So here we go:
Is there access to free internet and cable TV? Is there free international calling?
Is there a clothes washer and a separate clothes dryer or only a rack?
Who's going to clean the place while you are there? Will you be required to clean it before you depart?
What floor is it on? If higher than ground floor, are there stairs to climb or is there an elevator?
How is the kitchen equipped? Does it have both a fridge and a freezer?
A dishwasher? Both an oven and a microwave?
Does it have a walk-in shower or tub/shower combination? If the latter, does the shower wand hang on the wall, or is it in a cradle at the wall edge of the tub?
If you decide on a warm location, does it have an air conditioner? If you decide on a WA weather type location, what's the heat like? And if you stay there several weeks, will you be required to pay for utilities in some way?
About the medical:
Some of the locations you consider may be too small to have any easily reachable medical facilities at all. This would be a deal breaker for me.
If you take any prescription meds, you'll need to have enough to cover the time you'll be in Europe, plus a couple of weeks.
If you use any OTC meds or supplements, you may need to take a supply with you or find out what they are called where you are going. Keep in mind that those may not be available at all, may have different dosage levels or that what's OTC here may be RX there or vice-versa.
If you are on Medicare, it will not cover you in Europe or the UK.
If you have a Medicare supplement, it might cover some things but not all.
You may need to get extra insurance coverage, especially for emergency medical evacuation and repatriation of remains.
I've visited Europe in every month except February and March. In all my travels no matter where I was, the best parts of the trip have always simply been being there, so I understand a bit of what you're seeking.
Since you're somewhat apprehensive about the planning, I also recommend that you read and take to heart all the Travel Tips right here on this RS website:
https://www.ricksteves.com/travel-tips
To learn a bit about locations you might also take a look at Explore Europe: https://www.ricksteves.com/europe
Finally, is there any location in your family history or DNA that you'd like to get the "feel" of? On my first trip to Europe there were 2 places that felt like home but were nothing like San Antonio where I was from: Scotland and Scandinavia. Now 45 years later I know that I have substantial DNA similar to that of the people who live there. Too bad it's so bloody cold!