And don't forget about Ammazzacaffč

Thank you for the recent suggestions.
It seems that the winebar dei Frescobaldi (Via dei Magazzini 2-4/R) doesn't have an Aperitivo/Apericena as such but they do have a good selection of wines by the glass and a bar menu with snacks.
I haven't checked the other suggestions yet but I will do so in the next few days.

If you want a good selection of wines by the glass and a snack, Enoteca Pitti Gola e Cantina is the absolute best IMHO. You should stop there at some point on your trip.

I have now checked the bars/restaurants mentioned.
A little information about them for other/future readers of this thread
(I couldn't find any specific mention of Aperitivo for all of them) :

Rifrullo : Via San Niccolo 55/r
Aperitivo 19-22. 10 €

Rivalta Cafe : Lungarno Corsini 14/r
Aperitivo 19.30- 22.30

Negroni Bar : Via dei Renai
Seems to be permanently closed.

Zoe : Via de' Renai 13/r

Moyo : Via dei Benci 23/r

Kitsch : Viale Antonio Gramsci 1/5 r

Soul Kitchen : Via de' Benci 34/ r
Aperitivo 19-22 all days.

Caffe Dogali : Viale Malta 5
Aperitivo from 19.

Cafe de Paris : Piazza Dalmazia 7 r

Oibo : Borgo dei Greci 1
Aperitivo 19-22 everyday, 8 €.

Florian : Via del Parione 28-32/r

Se Sto : Piazza Ognissanti 3, in the Westin

Grand Cafe San Marco: on Piazza San Marco.
10 €. Aperitivo from 18.00.

Enoteca Pitti Golane Cantina : Piazza de' Pitti 16
As mentioned this is not an Aperitivo place but a
place for wine. They also have winetasting
events.

Ristorante & Winebar Dei Frescobaldi : Via dei Magazzini 2-4/r
No Aperitivo as such but a good choice
of wine by the glass and a bar menu
with snacks.

Mercato Centrale : Food court on first floor. Open 10-24 every day.
No Aperitivo but food, snacks, wine, beer all day

Ammazzacaffe : Seems to be not a cafe but the Italian word for after-dinner-
drink (aka the French Digestif/Pousse-cafe).

Sorry for any confusion, this was a bit of a joke. After the rather complete discussion of pre-dinner drinking mentioned above, I thought it only fair that there be some consideration of after dinner drinking. The "coffee-killer" is the drink you have after the coffee after dinner.

No problem - learned a new word and remembered that I had a mini bottle of Limoncello lying around somewhere.....

I have collected all the places mentioned in this thread in post 19 for future reference.

Just walked past a place today that had a sign out about aperitivo.
Grand Cafe San Marco on Piazza San Marco.
10 €. From 18.00.