Not as fast as you think. I’m a real fighter pilot (F-14), and the common belief that they’re lying about top speeds is backwards. The advertised “top speed” of a fighter is in the clean (no tanks, rails, or armaments) configuration, only useful for air shows and wowing politicians.
And even that’s done at maximum altitude, using the entire tank of fuel on one or two runs, then bingoing home on fumes. At maximum afterburner, the fuel consumptions of a jet engine is abysmal, and no one but an SR-71, which was designed to do that and only that, can sustain it for long.
And even that’s not for as long as you think; the Blackbird had to refuel frequently. So would a fighter flying at top speed.
Realistic top speeds are much, much lower than advertised. See this “Mach 2+” F-16?

It’s barely capable of going supersonic, if at all. But in that configuration, it’s extremely useful. In the “top speed” configuration, not so much.
The most I ever saw on my “Mach 2.34” Tomcat was around M1.6, and that was playing a high, fast bogey for another to intercept. This used a lot of my fuel, but we were done with everything else, and pointed back towards NAS Oceana.
No one ever gave me an unarmed, tankless plane and eight tons of gas and said “Go out and see how fast you can go!” So no – they aren’t hiding the “real” top speeds. They’re exaggerating them.

But it still was a blast to fly! Source of photo unknown, but I’ve flown that very plane.
So the answer is probably in the neighborhood of four hours going west-to-east (with the prevailing winds). Flying at “Happy Hour” cruise of M.90, and slowing down for one aerial refueling, and not keeping a big reserve for weather at the destination. Supersonic would require multiple refuelings, likely adding more time to the trip.
People are asking about Concorde and the F-22, both supercruising. Concorde did it by carrying an outrageous amount of fuel – about the same as a 400+ seat 747, while carrying only 90 passengers. The F-22 is impressive, but physics is physics.
There’s a lot of additional drag going that fast, so while it’s supersonic range is undoubtedly better than most, it’s still burning a lot of fuel cruising at Mach 1.6. Maybe that would be enough to make up for an additional refueling or two, but the difference wouldn’t be too great.

1 hour, 7 minutes, 53.6 seconds, Average Speed: 2,124.51 mph.
Other notable times:
New York to London, 1 hour 54 minutes, 56.4 seconds.
St. Louis to Cincinnati (crossing both the states of Illinois & Indiana), 8 minutes, 31.9 seconds.
London to Los Angeles, 3 hours, 47 minutes, 39 seconds.
Not an actual fighter per se, but military non the less.