Bologna Guglielmo Marconi airport

It's a great idea, particularly since you're coming from Arizona, so you have to change planes to get anywhere in Italy (coming from New York, I can get a nonstop to Venice but not Bologna).

Just look for "multi city" or "multiple destinations" on the airline booking sites, Kayak, etc. (US to Bologna as flight 1 and Venice to US as flight 2). Don't look for two one-ways, as that can be much more expensive. And do get these flights all on one ticket, so you're "protected" if one flight is late.

On another thread, Roberto posted that British Air has several flights a day from Heathrow to Bologna, and there are nonstops from Phoenix to Heathrow, so this should work well.

Bologna airport is easy. Easiest would be to catch a taxi to the train station or if you are staying (recommend!) take a cab to your hotel - you'll be tired, you are not familiar with the city. It's not expensive, and it will save time and a headache.

I'd recommend spending at least 2 days, in Bologna. Arrive, sleep, take a food tour, sleep, then go on to Venice.

Totally can recommend Alessandro at Italian Days Food Experience. 150E for one person for a full day FUN food tour. It's all about DOP and slow food. http://www.italiandays.it/

BEST money ever spent in Italy. The pick you up at your hotel at 7AM feed you all day while you learn and drop you off at your hotel at 4:30....totally stuffed with food and wine and love.

Bologna itself is a wonderful quiet town, easy to navigate....and has a few great towers, one to walk up and see all of the the city and the countryside (3E to climb)

I would also check the price of flying to Milan and taking the train from the airport to Milano Centrale station and then transferring on to a Freccia train to Bologna which is only 1 hour away with trains every 30 minutes. Base fare is 40 euro, with the 12 euro airport train, if you save more than $60 on air, that is the way to go.
Bologna airport is not too far out of town, so you can taxi from there.

The thought of getting to a train station and onto a train after a long flight is exhausting.

What I find exhausting is waiting around an airport for several hours to get on a little puddle-jumper airplane in a cramped seat, when I could be riding in a comfortable seat on a train.

I used it last month for a flight back home. Efficient airport. Frequent buses to central Bologna for, if I remember correctly, EUR 6. And Bologna is a most agreeable lively city. Well worth a day or two. And it's a good base for a daytrip to Ferrara or Ravenna.

Since you fly from the Far West (like me) I strongly suggest that you consider a non stop flight directly to Europe and avoid a lay over in the East US. That will save you time and aggravation, also because of the possibility of delays and missed connections. Unfortunately PHX has only one such non stop option to Europe. It's with British Air to LHR. I exhort you to consider it nevertheless.

My other suggestion is to start with Venice first, primarily because flying back to America starting from VCE is a hassle as the VCE airport is not near the historical center of Venice and finding your way to it (partly or entirely via boat) will likely require you to get up in the middle of the night.

This is particularly true if you fly BA and you want to make that morning flight from LHR to PHX. There is only one daily flight from VCE to LHR and not early enough for you to make it to London on time.

Bologna (BLQ) has 3 dailies to LHR with BA starting with early morning. BLQ is also near the city center, and you can reach it in 15 min by taxi from any hotel.

So my suggestion is to fly BA from PHX to VCE going. If that doesn't work since there is only one flight from LHR to VCE, then you can try Milan Linate (LIN) (BA doesn't fly to Malpensa and in any case LIN is closer to the Milan Central station. From Milan you can take a train to Venice.

Your return would be from BLQ to PHX via LHR, with BA.

You could also consider a flight in and out of BLQ. From BLQ to the Central station it's only 15-20 min by taxi or shuttle bus. Then from Bologna Centrale to Venezia S. Lucia it's a short high speed train ride (less than 1.5 hours).

If instead of LHR you decide to fly via JFK, EWR, ATL, Delta and United have non stop flight to VCE but not BLQ. There are no non stop flights from BLQ to North America but Bologna is very well connected with all major European hubs.

http://www.tper.it/content/linea-blq-aeroporto-stazione-centrale#airportENGstation
Here is a schematic diagram of the bus shuttle from the Bologna airport to the city core and the main train station. Because there are traffic restrictions in the centre during some tourist months, stops on weekends may differ from weekdays.
Buses in Venice run from the airport to the main bus terminus near the island causeway.
http://www.veniceairport.it/en/transport/bus.html

As suggested, a multi-city itinerary makes sense to save both time and money. It doesn't matter too much whether you arrive at Venice or Bologna. In either case, the departure for the return trip will probably mean an early-morning flight to leave time to connect to the trans-Atlantic flight west. Venice may offer slightly more civilized wake-up requirements. A good place to compare is www.itasoftware.com which is run by Google for many (not all) airlines. Its multi-destination function will give a good overview although it does not itself sell tickets. The site will do a more efficient job of sorting out connections than you can on your own.

Certainly do an open jaw ticket, flying into one location and out of another. We ended our trip last month in Bologna. It's a great place to spend 2-3 days. BLQ is very close to the city center. It took only 15 - 20 minutes from our hotel. We had an early morning flight (6 AM) out to Amsterdam. The airport isn't large, and was easy to navigate through.

Good luck with your planning!