Some parts of The Four Seasons are marked as having a tempo of "Allegro non molto" (Fast not very?), however, I do not see this tempo as being one of the standard ones. There is normally Allegro (Fast) and Molto Allegro (Very Fast). What is Allegro non molto?
On one of my metronomes, allegro is marked as 120-168 bpm. On another, it's 150-178 bpm. No great help!
Back in the days when bpm wasn't the datum point, composers would use (vague) tempo names to give a sort of ball-park speed for their compositions. Partly because that's all there was, partly to afford performers some leeway. After all, most 'classical' (serious) pieces would (and do) fluctuate a fair bit even during the same sections.
So - allegro is 'quick'. But Vivaldi didn't want it too 'quick', as often quick pieces have the tendency to accelerate to 'even quicker' as they progress.
Thus - allegro (quick) non (not) molto (much, very) is what Vivaldi hoped would be moving along, without appearing to be in too much of a hurry. Still giving, actually, plenty of leeway, according to my metronomes...