This doesn't even necessarily have to imply relocation abroad. Just being in the right city within a single country can make a hugely positive difference vs. being in a wrong city. The same principle applies regardless of whether you're abroad or at home.
I absolutely loathe the UK and find most of its cities and towns horrible due to their hideous architecture, bad vibe and antisocial people, but there is one single town in the UK — only one!!! — that is the exception and where I feel happy and at home. It's the same town I mentioned in my recent thread on "city egregores", the one situated about 7 miles from my hometown and whose football (soccer) team I've followed since being a kid. It's a market town of about 100,000 people, historically a mining town, with nice architecture, a strong community spirit and friendly people.
I often come here when I need to buy something and always find the place noticeably more pleasant than other UK cities and towns, but right now I'm temporarily living here since I'm looking after a friend's pet while he's on holiday with his girlfriend and I find it even more awesome.

To begin with, unlike most UK cities, the town has beautiful architectural styles, including classical and Italianate. Even its modernist buildings are rather well-made. Bright stone buildings and paving predominate. A few buildings feature Greco-Roman columns. Some areas feel more like a Mediterranean country than the UK. The vibe is amazing and I always feel uplifted and energized.
Then there are many cool things like 80s-themed nightclubs, Asian and Turkish restaurants, a Brazilian bar, shopping centers, a cinema that shows all the old classics, a few very nice and well-kept public areas such as the Town Hall and central plaza, and a state-of-the-art college. It's simple but decent for a town of its population size.
Speaking of population, the people here are really nice and friendly, so much so that I even forget that I'm in the UK. They're neither paranoid nor antisocial; often strike up conversation with you in the street; and are surprisingly helpful. Yesterday I was on the phone talking about how I needed to find a pet supplies store and a passer-by stopped and went out of his way to give me detailed directions. This place still has community spirit.
People even speak a better form of English here, one that's folksy and traditional, not like the faggy and aesthetically repulsive linguistic varieties spoken in most parts of the UK.
All in all, I feel a lot happier and mentally well here than I usually do in my bumpkin-filled hometown. I feel more relaxed and motivated to do things as well as less socially anxious. My feelings of misanthropy have also gone down substantially.
The right city makes every bit of a difference. It can determine whether you wake up vibrant and full of life or chronically depressed and hating life. If you aren't in a place that's suitable for you, you'll never find true satisfaction.
The right city can either make or break your HA experience too. You might find your own personal Shangri-la in a foreign country and find lasting satisfaction (like I did with Valencia) or you might choose the wrong city and end up thoroughly disappointed. Right location is essential.