Tips for 3 Months in Europe

If you want to consider a house exchange, you should start looking into it now. We have found that it takes quite a while to actually find and set up an exchange. It's true you live in a very desirable area, but the vast majority of exchanges are sought by families with children and, therefore, for school holiday times. You can browse the listings of most of the exchange companies to get a feel for what's available.
Another vehicle might be university and college housing offices, e.g., UCSC and CSMB. They often have visiting teachers and researchers needing short-term accommodations.
Portugal would certainly be cheaper than Italy; but both it and Spain are also more remote from the rest of Europe. In these initial stages of planning, you should take some time to reflect on what you really want. No point in being in Portugal if you really want to be in Italy.
And as has been said many times on this forum, don't forget to keep in mind the Schengen rules on long stays.

For me, Italy would be more desirable as a base, smaller less touristy town probably cheaper. My strategy would be to look at the main Rail lines, finding a smaller town with decent service. I am partial to North of Rome, but the main line South might offer some interesting options as well. With decent transport, you can day trip or overnight easily to really fantastic places. Portugal has it's own charm, but I think you would find yourself more limited to your immediate area, may be my take, but in planning I found transport within Portugal and connections with Spain more difficult than Italy.

I think first you have to give up the idea of getting a house in return for a house. Owning or renting a house is far more expensive in Western Europe than in the U.S. There are very few people who can actually offer you their own house, just because they don't live in one. Most people over here live in flats, even in rural areas. So, if you throw your house in, expect someone offering you her or his flat in return. And that's not meant as a rip-off.

To emphasise the comment above, Julie, I hope that you are aware of the laws regarding longer than 90 days in the Schengen area for Americans.

Those are collectively referred to as the Schengen rules, and they are strictly enforced. I mention this because the title talks about 3 months, but the text of your question talked about "several months" which to me is more than 2.

I agree, settle where you want to be, not where you have to go to.

If Italy is your first choice then go with it as there are no substitutes.
U may need to reduce your travel time there to meet your budget.
Perhaps u could consider a combo apt rental and convent stays in italy.
Perhaps one more north another more south. Italy is quite large for some train day trips.
Start with a map and highlight what you wish to visit. It may help u hone down a few poss areas to focus on.
Have fun, the planning can be alot of fun.

I do not think you need the expense of a vehicle, at least not for the entire stay, if you choose a town on a rail line. Florence is certainly a possibility: small enough to get to know but big enough to have services. Florence is on the high speed rail line and also has connections by bus to many nice Tuscan towns. Monthly rentals usually cost less. You can negotiate a bit when you commit to a longer term. We recently did 4-week stay in a small town and negotiated down from €120/night to 100 as a result.

A source I have had positive experience with is www.sabbaticalhomes.com.

House swapping is an option, but may be difficult to coordinate if you are away for three months.

Many European accommodation places offer good value long term winter rentals, but these are usually for November through to March. September is only just off high season, so you won't get any monthly discounts.

The Algarve in southern Portugal would be a good base to explore Portugal and southern Spain. Rather than pay rent on somewhere, then travel elsewhere for two weeks, paying double rent, why not move base and have say 4 weeks in each location. I am renting a spacious one bed apartment in Cabanas on the Algarve in March for £600 for 28 nights (paying in GBP not euros) through Owners Direct. In September, the same apartment is £450 per week! You will get much better value accommodation if you move the dates of your trip.

Hiring a car in Portugal is very cheap off season. This year, we paid an additional 30 euros to take the car into Spain for a week. Another benefit of Portugal is that they eat at "normal " meal times, rather than lunch at 3pm and dinner at 10pm or later, as in Spain. Portugal is much better value than either Spain or Italy.

I'll offer a different perspective!
Our family has completed many long-term home exchanges in Europe - anywhere from 3-4 weeks to 9 weeks. They are not difficult to arrange and you should have no problem finding other retirees who wish to exchange with you. We have exchanged with families, couples, and groups of couples over the years.
For a Fall 2017 home exchange you could start sending out inquiries now but we typically start 6 - 8 months before our planned trip. Some people plan a year in advance but most start thinking about it 6 - 8 months ahead of time.
You should have NO trouble exchanging your home in Monterey! So many people in Europe are interested in the CA coast. Once you put your listing up you'll get lots of offers.
A few ideas for lower cost destinations in Europe.... Some parts of Italy are expensive but some are downright cheap...Sicily comes to mind. We spent a month on a home exchange in the Czech Republic last year, in a village outside of Prague, and it was a bargain! You can live very well there for very little money. This is true of most eastern European countries...they are beautiful and very interesting to explore. Poland, Hungary, Slovenia, and Slovakia might be places to look into. Parts of France are also not terribly expensive...Languedoc and Herault are gorgeous areas with a nice coastlines, spectacular villages, and wine!
About a car...we almost always exchange cars with our home exchange partners, further reducing our expenses! Our insurance covers our guests and they make similar arrangements for us with their vehicles. It will save you a bundle! Not everyone is comfortable with this but we have never had an issue.
Like others have mentioned, be careful about the Schengen rules. You can only stay in the Schengen Zone for 90 days out of every 180 (a very simplistic explanation). If you with to stay longer you must leave the Schengen Zone. A good place to do this is the UK...if you are an American citizen you can stay there for 6 months as a tourist. Parts of the UK are quite expensive but, again, if you go to some of the smaller places in the countryside it is entirely affordable.
Let me know if you have questions about home exchange...it's our favorite way to travel!

Side-tripping from a home base is only as affordable as the destinations are close. After a while, I would get tired of retracing my steps. If you want a wider variety of side trips, then you probably need a variety of home bases, whether for a month, or two weeks, etc.

For connecting countries, budget flights can be quite affordable within Europe; see www.skyscanner.com. Most service and competition is between big cities, but Pisa is an example of a smaller town that's served by the budget carriers.

I've done a long-term car lease through Peugeot (these programs are all based in France, with a few neighboring delivery locations), but it's not necessarily cheap. See also https://www.ricksteves.com/travel-tips/transportation/car-leasing.

If a home exchange comes with use of a car, then all the better.

I would look at 3 weeks in each of 4 different locations (preferably all transport hubs).

Lots of options - you'll need to decide which best fits your own personal interests and desires. Yes parts of Italy can be very expensive and popular, but there are plenty of small towns few people have even heard of and still near Rome or Florence or other popular cities but could be a nice place to settle in. Go over a map and do some research online.

The same applies to Spain. Portugal is very remote as others have said, and might not be the best place to get away for a few days. But there is lots to see and do in Portugal and with a car you could see parts of Spain easily too.

I would consider the idea of having a few different bases but if you are the type to want to just relax for a couple of months with occasional day and side trips, don't let us discourage you.

If you are interested in house sharing, I would look into organizations or websites where that is a focus. This forum is more just European travel advice, and you've already gotten very conflicting information.

Right now, I'd say the best budget locations in Europe are Spain and Poland. I haven't been to Portugal so I don't know.

I'd throw out Portugal because it's just too far removed to provide convenient travel to the rest of Europe. I might also throw out Poland because it will be cold by about mid October.

I wouldn't do Italy for a couple of reasons. Yes, it's more expensive. I'll get scorned for saying this but you are also more likely to run into scams or simply unsatisfactory conditions that the owner/company you work with has no intention of resolving. For better or worse, that's Italy - you either laugh about it or cry. If you can't laugh, you probably won't love Italy.

I'd stick to Northeast Spain, maybe Zaragosa, for something that's not too difficult to travel from but also affordable and has the amenities you need. From Zaragosa you can fast train to Barcelona (maybe the most expensive Spanish city) and connect from there.

You may find that picking something in the south half of France may be the better overall choice. It will be more expensive but the weather should be decent and you will save a lot of time every time you travel.