"Speedstream" by James Lovegrove, Interzone issue 163, January 2001.
Greek as «Ταχύτητα Διαφυγής» (which literally translates as "Escape Velocity"), 9 issue 154-156, June-July 2003.
9 was a weekly comics & SF supplement to the sadly now-defunct daily paper Ελευθεροτυπία. Some example covers can be seen at http://www.eugiefoster.com/cover-art/9_magazine, and I discovered that the magazine once produced an anthology, 9ΕΦ. The Lovegrove story doesn't appear to be in it. The title 9ΕΦ, incidentally, is probably from the Greek words for "SF", «Επιστημονική φαντασία».
My information on the English version is from ISFDB; on the Greek, from James Lovegrove's
web page https://www.jameslovegrove.com/books/. There are slight typos in the title
given there: «ξ» should be «χ», and the words are missing their stress accents. ISFDB doesn't
mention this translation.
The protagonist used to travel a lot, mainly using high speed media like aircraft.
"Stoneham journeyed on.
Now he was aboard a train, heading for somewhere called Capa Douf.
Now he was on a bus, lumbering through lush green valleys towards
Now he was in a hired car, driving across a vast volcanic plain like a section of moonscape brought to
earth. One thousand miles ahead: Fathomopolis.
Now a boat. Then a plane. Then a train again. Then another plane."
It was established in the story that as he traveled more frequently and with more speed, he would
gradually cross over towards (sort of) higher planes of existence (and that everyone in the setting
could do the same, although most people simply didn't bother). These higher planes of existence
were apparently still Earth, but the environments and the inhabitants
were increasingly more alien and life in them was increasingly luxurious.
If you were doing well, you graduated through the levels without being fully conscious
of doing so. An imperceptible shifting-up of gears. Only when you reached your next
destination did you realise that the place you had come to was not in quite the
same world as the place you had left behind. Something had changed, something
fundamentally indefinable and indefinably fundamental. Somehow you knew — though you
could not put your finger on how, exactly — that where you were was universally
better than where you had been."
An example: "Marn Werev: reminiscent of a Belgian city. Flat, planned, orderly, gleaming, greened."
As far as I recall, the protagonist's goal was to reach those higher levels (either for the luxury or
for some other reason I can't recall).
"And you kept on moving, because that was what you did, what you had to do. That was how, as a Fogg, you
shook off the past. You moved on."
"Once more, Continuum beckoned. The ultimate goal of every Fogg. The final destination. The purpose. Nobody knew
what it was. All that was known was that a few Foggs had disappeared into it. Had accumulated
so much Speed, risen so high up the levels, that they vanished out of existence.
An abstract concept. Perhaps an illusion. But this theoretical oblivion had been given
a name nonetheless: Continuum."
If he failed to maintain his "speed" for too long, he would fall back to lower planes of existence, with
more familiar characteristics and significantly lower quality of life.
"It took guts to Slow on purpose. [...] He arrived at San Barcino in a cold sweat, with a lump
in the back of his throat that he could not swallow down. Once this had been a spectacular
city, you could tell. Vibrant. Twenty-four-hour. Now: lost and old and succumbing
to crime and vermin. A cloud settled over Stoneham's soul. Things
were only going to get worse.
Palgray. Like every superannuated British seaside resort rolled into one,
perched at the edge of a vast, leaden inland lake. Bursts of liveliness
here and there, but the closed-down shops and restaurants outnumbered
the open, and the residents outnumbered the visitors."
His wife had died some time ago and her grave was apparently in the lower planes.
He did visit her once
near the end of the story, before starting to build up "speed" again.
"Joanna's ashes had been sprinkled over a corner of the garden
of remembrance at the Green Lawns Cemetery just outside Guildford.
A tree had been planted there in her name. A silver birch, now twelve
feet tall, whitely spreading its wings. There was a brass plaque
on a small concrete plinth set into the ground at its base: