Hi everyone, it's me again!

I'll be visiting Florence in the beginning of May and am asking you gentlemen what collections or sites with medieval era stuff are there to see? We will probably be visiting some other towns in vicinity too, so if there is something worth seeing around there, let me know please!
I heard the Stibbert (or something?) museum has quite a nice collection, are there any others?

Thanks in advance!
Miha

One obvious candidate is Santa Maria del Fiore, the cathedral with the dome. You should read the fascinating history of how Bruneschelli built it in the 15th century if you haven't done so already, particularly if you get the opportunity to see it in person.

http://en.wikipedia.org/wiki/Florence_Cathedral

I can't help you with arms and armour specific attractions, sorry. I haven't actually been to Florence yet, though I'd like to! Have fun in your travels.

The Bargello!!!!! The Medici armoury is there. Please make some photos from several composite bows :D

It's just until 14.00 pm open!!!

The Stibbert weapons museum, obviously

http://www.museostibbert.it/en

:idea:

I was able to visit this past September. As mentioned already, the Duomo, but it is impossible to miss it. The climb to the top is really worth it . The Accademia for Michelangelo's David, as well as the Uffizi Gallery, and Galileo Science Museum.

One thing that I found really helpful, pick up Rick Steve's guide books. They saved me a lot of time, that would have been spent in lines as well as some money.

Big thanks to everyone, your suggestions will definitely help a lot!

Everyone has posted the places I would suggest. I second the recommendation for Rick Steves' Florence guidebook. It's his best one and full of tips to make your visit easier and more affordable. If you can make it to Pisa, do so as well.

Be aware that the Stibbert only does guided tours. My tour consisted of a school group of twenty 4 year olds, two bored teaches and myself. The guide couldn't understand why I was wanting to look at the armour so closely. An interesting visit though. But a lot of restored armours.
Most large Italian towns have good museums that have arms and armour
Other towns to look at I'd suggest Mantua. An interesting town with not so many tourists. Great armour in the diosceses museum, remains of tournament frescos in the ducal palace.
. Milan has several museums with armour, Brescia has a good castle museum, Venice has the ducal palace armoury and other interesting museums.
If time is plentiful the pilgrimage to Schulderns to visit Churburg castle, (guided tours only) is worth it if nothing else the change in cultre as this area is very Tirolean with German being the predominate language.
Andrew

I really enjoyed the museum of Galileo, while I was in Florence. It is not so much about the man himself but more to do with scientific inventions and astronomy.

http://www.museogalileo.it/en/visit.html