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I too have a Honda Jazz... 2007.
5 speed manual, i do not believe in skipping gears usually.
For constant acceleration, change up gears as early as you can, holding 2nd gear to 50kmh for example means you are holding that gear too long... Unless you are rocketing up to 50kmh at optimum load.
On my jazz, city driving i upshift really early and keep the engine loaded. With careful use of throttle (not too much, not too little) i have these shift points:
1>2nd ~7-8mph (1800>1100rpm)
2nd>3rd ~15mph (1700>1200)
3rd>4th ~20mph (1400>1100rpm) (going off memory all these rpm figures so maybe wrong)
4th>5th ~25mph
These are ultra low RPMs for accelerating... but using torque pro i'm not using too much throttle (which would cause engine knock) and acceleration is not awful.
I've achieved indicated 70+mpg (UK) just around town at 3am after dropping friends home. The jazz seems to really like low RPMs (mine's a 1.3 idsi)
Effective use of DFCO also is good, you need to be above 1500rpm to activate DFCO in jazz, so i find myself dropping a gear / dropping 2 gears when i need to slow down. (rev matched too... dragging the engine rpm up with the clutch kills momentum)
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