The usual things you would consider if relocating within the US--cost of living, crime, strength of the economy, political stability of (local) government--all apply. But if you dig a bit deeper, there are some additional things to consider. The 8 that I list below are decidedly negative; however, they can be outweighed by the many, many positives.
We moved to southern Switzerland for a job opportunity for me and then after a half dozen years FIRED here. Now, 6 years later we love it even more than ever. I would pay attention to several key issues:
1. Exchange rate. We chose to maintain our US investments (best market in the world, highly transparent, abides by the rule of law). We move funds during the year from the US to our Swiss bank (NOT that kind of bank). In our case the US dollar has, at times, fallen appreciably below the Swiss Franc (CHF), which is highly overvalued as well. So, we have to maintain a cushion in budgeting. I create our budgets using the mid point between best and worst cases in the Dollar/CHF from the last five years. This generally produces a surplus at the end of the year, which is nice. I also track trends in the Dollar/CHF exchange pair, and move quickly when I perceive an opportune time to move some money. This requires daily tracking; but I have grown to kind of enjoy it so far. It's like a game of wits and I have become good at it.
2. As Alan mentioned above, there is a lot of confusion among even so-called experts about which income is taxable only in your country and which is taxable in the US, or both. The "savings clause" in the US treaty with Switzerland (which is very much like that of most other countries) says that at the end, basically ALL income is potentially taxable by the US, making most of the favorable paragraphs in the treaties null and void. Arggh. The only good thing is that you get most (sometimes not all) of the taxes you paid in the new country counted against your US tax bill. Also, it depends on whether your new country's tax rates are higher or lower than those in the US. Swiss taxes are overall lower than the US, so we usually end up paying the IRS as well as Switzerland. It can be complicated on both ends, so we pay consultants to do our taxes.
3. The Patriot Act signed into law just after 9/11 specifies that holders of mutual funds and brokerage accounts in US banks must be resident in the US. So, many US expat investors had to sell their holdings, pay capital gains, and move them to the new country. Except, see below for the gotcha on this. One way around this is to use a friend's address as your own...but isn't a perfect long term solution. Another is to utilize a remailing agency in the US that gives you a postal address in the US. Just be sure it is in Texas or Florida or any other of the very few which do not have a state income tax.
4. Banking. The US extends its long arm rather forcefully into the financial affairs and systems of countries where expats live. We must fill out an annual form, the FBAR, under penalty of law, detailing all of our bank accounts--account numbers, highest value in the preceding year, name/address of the banks. OK, I'm fine with this as we are not rich, money hiders; BUT, two things irk me: the US refuses to reciprocate with all these countries. So, it is well known, for example, that Brazil has been trying for years to get the US to turn over information about Brazilians holding cash in Miami banks, with no result. Second, and this sounds petty, but the form we fill out is part of the Financial Crimes Enforcement Network (FCEN) in the US government, and this is highlighted on the web page where you fill in the form. It irks me no end to look at this form and it's parent office that I am reporting to. I am no criminal.
5. The aforementioned long arm of the US IRS reaches into the financial systems of your new country with burdensome annual reporting requirements on your accounts (savings, payment accounts, mortgages, etc.) such that in many countries, Switzerland included, most banks, rather than comply with the costs of doing this reporting for their relatively few Americans, instead just forced them out as customers over the last decade. In some cases, they cancelled local mortgage loans, making the outstanding balance due immediately. Also, they stopped taking new American customers. In our case we were asked to cancel our account at a major Swiss bank by the following day (!). We were saved by the Swiss Postal Service, which serves as a bank as well. They are required by charter to serve any person resident in Switzerland, regardless of nationality. It turns out to be a great bank as well. I think that UBS also has created a "walled off" section for American customers.
6. Going back. If you decide to return to the US, you may get a nasty surprise. Some states (e.g., California) will charge you with state income back taxes for the intervening years, unless you prove conclusively that you never planned to return. Even maintaining a safe deposit box in your old state may be enough for them to charge these back taxes. So, be aware.
7. You, like the other 7-8 million of US expats will not longer have any representation in the US congress. There is an expats advocacy group trying to help with things like taxation--only the US, North Korea, and Eritrea tax their expats, no matter where they live, no other countries do--without congressional representation we are out of luck.
8. Last, depending on where you are located, friends and family may find it harder to visit you (and vice versa, of course). On the other hand, we've come to find that many friends and family find the prospect of visiting us in Switzerland to be irresistible, at least once anyway. So that's nice. We even offer them free accommodation at Hotel Barnfeather!
All of these negatives may seem overwhelming at first; but for my wife and me the advantages of living in a beautiful country in the middle of Europe with easy travel access to so many places we love to visit, plus the personal safety, excellent health system, and sane government it offers makes our choice mostly a slam dunk. We just budget carefully and hope for the best!
I should add that in our original FIRE planning, we in no case had listed Switzerland as our RE destination! It just worked out that way and we found we didn't really want to ever leave.
I hope this helps.
-BB