What types of food were available during the Renaissance Era in Europe
during the 1300-1500's, especially in Italy?

It's easier to say what was NOT available to the Italians in the
middle ages. I compiled a list of such foods some years ago in an
article for the Company of Saynte George, Dragon issue no. 1 which can
be found at:

http://www.companie-of-st-george.ch/dragons_1.phtml

These are:

Apricot
Artichoke
Aubergine (eggplant)
Beans other than broad beans
Brussel sprout*
Carrot (orange-coloured variety)
Cauliflower*
Celery
Chocolate
Corn
Courgettes (squash)
Lemon*
Melon*
Mulberry*
Peach
Pineapple
Potato
Pumpkin
Rhubarb
Salsify
Shallot
Spinach
Swede
Tomato
Turkey
Pepper

An asterisk denotes food that may have been available in southern
Europe but not in the north, or foods that were so rare as to be
available only to the courts.

If by any chance you're looking for cooking and recipes, I recommend:

'The Original Mediterranean Cuisine: Medieval Recipes for Today' by
Barbara Santich (Prospect Books, Totnes, Devon 1995. ISBN 0907325 59
9)

"What types of food were available during the Renaissance Era in Europe
during the 1300-1500's, especially in Italy?"

The European Renaissance is generally agreed to be 1400-1600 give or
take 50 years at the end.