Two months for long, slow honeymoon

You may find some useful connections here
http://www.myitalianfriends.com/

How exciting!
Just some general suggestions: Try to narrow down what areas you are interested in, since the cuisine is so regional.
We find Italy much more affordable when not in the main cities or tourism concentrated places like the Amalfi coast. So, if you are willing to be elsewhere, then your money should go farther. I would share some details about your budget for feedback though. Sometimes rentals can be surprisingly affordable.
However, being off the beaten path often means having more need of a car--if you are spending long stretches of time, this is probably less of a factor. Unfortunately, another downside is that it will be August--I'd head to inland mountains for that part!
congrats and good luck!

As a chef is your fiancée interested in the farm to fork, slow food movement? If you want to do more than just cook maybe a short, working, farm stay in Italy would interest you. There is an organization called WWOOF which helps people connect to small, organic farms needing short and long term help. https://www.wwoof.it/en/. From the link page, go to the link that says Hosts and you'll see some regions in Italy and what type of arrangement the owners seek. We've had children of friends do this in Europe and they enjoyed the experience.

EDIT: since these are small working farms some are more accessible than others using public transportation.

We love wine, cooking, coffee, people, and the outdoors.

Try to stay in a place no LESS than two weeks. That means, perhaps 4 bases for you and minimal transfers.

Small towns are much less expensive than the tourist areas, as others have said. Some to try:

• The Dolomites. Especially in June or July, before the more expensive month of August. I know from experience you can get an apartment for 100 Euros per night, maybe less. The outdoors here is magnificent and an escape from the heat in the cities. We like the Val Gardena particularly. No car required and your lodging will give you a pass for the buses that run through the valley.

• Umbria. Lots of small towns to choose from. Harder without a car, but doable.

• Liguria, outside of the Cinque Terre.

Have you ever looked at house-or-pet-sitting? You might find a match at www.TrustedHouseSitters.com.

Another source to try is www.SabbaticalHomes.com. These are short-to-long-term rentals generally by academics who are away teaching.

If you are set on Italy, consider less expensive Sicily or the perhaps even cheaper Sardinia.

I would caution you to research whether working in Europe would be legal unless it is completely volunteer work - meaning you get no consideration in return, whether it is lessons (and as a chef, that would be professional benefit) or room and/or board.

You might consider a cheaper country - perhaps Hungary (great food, great wines, outdoor activities).

Another warning about exchanging labor for goods or services.

If it were me, I would spend two weeks in Sicilia, two weeks in Emilia-Romagna, two weeks in Liguria, and two weeks in the Veneto or in Tuscany. This will give you a variety of regional cooking. Choose a smaller city and you will be surprised at how affordable an apartment or B&B will be.

Another vote for the Val Gardena. Spent five nights there last June and returning again in 8 nights next June. Check out their website valgardena.it, very informative.

Another vote for Sicilia! The food, the wine, the scenery are just amazing! It's also much less expensive than most of the rest of Europe.