Europe in July for 9 days

Well you're going to get warm/hot temps wherever you go in all likelihood. Focussing on your two main listed cities, Prague is really an awesome place - the architecture blew me away. You could pair Prague and Vienna quite nicely and have plenty to do. They are are easy 4 hour train ride apart. I'm assuming you actually have 8 nights in Europe. You could give 4 nights to each city and have an great time.

If you're leaning more towards Venice (my favorite city anywhere), you'll find that 3 nights is enough and there are definitely less sites to visit...more just enjoying the atmosphere and a few must-do sites. You could pair Venice with another high-site city with cheap flights on one of the low-cost carriers - Budapest, something edgier like Istanbul since you've seen a lot of places.

Iceland is a fascinating place to visit - lots of outdoorsy stuff to do, great food, very interesting landscape, good museums and other sites, and doesn't get the least bit hot in the summer (the sun doesn't go down either).

I would suggest Prague and Budapest as a good pair of cities to visit - 4 nights in Prague and 5 in Budapest. A day trip to the countryside nearby for hiking or enjoying the small towns and scenery. Lots of stuff to do in both to keep you all busy, lots of young people in both with lots of nightlife, bar and cafe culture, your young adults should enjoy both. Train wouldn't be best between these two since it's a long ride (7 hrs or so) but there are budget airlines that fly non-stop between them and probably cheaper than the train.

Other option would be Prague and Vienna. Shorter train ride between them (4 hrs), lots to see and do, day trip from Vienna to the Wachau Valley, or to Melk on the Danube boat/train outing. Also possible to do day trip to Bratislava, Slovakia easily from Vienna. You could also plan a stop for 1-2 nights in Cesky Krumlov between them for lots of outdoor activities - canoeing or kayaking on the Vlatava River that runs through the town.

Possibilities are nearly infinite, and all the suggestions above sound good to me. I'd expect brutal heat south of the Alps unless you're at altitude, but you might get lucky.

I've made a number of summer trips to Switzerland (none recently), and I'd say the weather is unreliable. You have to plan for all eventualities. It can be 50ish (F) and rainy at the same time--I'm not talking about the mountains--which is pretty uncomfortable if you have only summer clothes. Cool, rainy weather can move in and stick around for 4 or 5 days. Some areas tend to be sunnier than others, like the Ticino. Another consideration is that your family sounds rather sight-driven, and Switzerland to me is more of an outdoor destination. There are museums, but that's not what I think about when I plan a trip to Switzerland.

My first thought was Venice coupled with some other spots in northern Italy -- perhaps a few of: the Dolomites, one of the lakes, Bergamo, Ravenna (fabulous mosaics), Verona, Bologna (museums), Padua (Scrovegni Chapel). Even if the heat is deadly elsewhere, it will be comfortable up in the Dolomites. Bolzano (larger) and Bressanone/Brixen are both nice bases to get up into the mountains but are pretty much as hot as Venice. If a heat wave hits, you'd have to get into the upper valleys to cool off, but that's generally why people go to that area, anyway. Bolzano has a number of museums to provide a bit of a culture fix. In Bolzano and Bressanone you must be sure your hotel has air conditioning; some otherwise nice places (at the 3-star level, at least) do not.

Zagreb is a very interesting city with a good selection of museums (I'm not suggesting it's the equivalent of London-Paris-Rome in that regard). Attractive architecture in the older part of town and lively atmosphere with lots of young people. Could be coupled with a visit to the Istrian Peninsula; expect lots of other tourists there in July. Or you could combine Zagreb with Ljubljana, Slovenia, smaller but also with interesting museums. English is widely spoken in Slovenia and Croatia, if that matters.

Many people have said Budapest is their favorite European city, so I'd take that as a very serious recommendation.

There are many limitations in your ques. if Prague is a must see, which I love, then how about pairing with Berlin? Venice - Ljubljana-Zagreb? Dolomites? Lauterbrunnen/Mürren and also dip into Austria? Sweden and Norway are great if you don't mind paying way too much for alcoholic beverages. So many wonderful choices.

Your college age kids wrote off two whole countries based on what actual knowledge that there will not be enough to do...stunning . You only have nine days . Many folks consider either Ireland or Scotland worth more then that...

You children are so lucky their parents continue to pay to take them on lovely holidays.

My 19 yr old will be backpacking aroung there in a few months on her own with friends, they managed to do all the research and save all the money themselves.

Why dont you tell your kids to come up with intinerary this year,,least they can do is contribute some research equity..then they will be happy, and gain some experince.

Sit back and let them do the work

I would add Venice and Lake Como (Varenna) to your itinerary. Venice is an amazing city. I am sure you can avoid the heat by traveling on the ferries in Lake Como. If you get bored with one town, just hope on the ferry to another.

We heard that Switzerland can be rainy in the summer. Not sure if this is accurate.
You can check weather met websites for climatic data. Such as:
http://www.climatedata.eu/climate.php?loc=szxx0033&lang=en
Statistical climatic data for Zurich for July: 12 Days of Precipitation

http://en.climate-data.org/location/2110/

Even the driest month still has a lot of rainfall.... Most
precipitation falls in August, with an average of 132 mm.

(July has an average of 129 mm of precipitation. January is the dry month with only 65 mm of precip.)

If July has 129 mm with 12 days being rain days, that's an average of 10.75 mm of precipitation for each of the 12 days of rain. In American units, that's about 0.4 inches in a day. No wonder why the scenery is so green.

If you want to see Venice, combine it with time in the Dolomites. You will all love the scenery, the hiking and mountain biking opportunities are endless. If you have 8 nights, 4 Venice and 4 in the Val Gardena of Italy. You can do this all by train and bus.

Yes, Venice will be warm...Use the mornings and the evenings to your advantage--everybody up-and-out before the heat comes on! Go to the islands, hit the beach at Lido.

I'm not sure why your kids think there would not be a lot to do in Ireland or Scotland, yet you say you like hiking, culture, restaurants and bars.... off the beaten path places. These countries abound in these things! A few years ago my family and I drove from Dublin across Ireland to ring of Kerry and Dingle and it was one of the most beautiful places I've been to. We loved the countryside, iron age forts, castles, great pubs (& Guinness), music, and friendly people. Since you are going in July, the weather might be nicer there than in Italy.

My reaction to your question is the same as the last two - that Ireland and Scotland have a great mix of sightseeing, hiking opportunities, and costal breezes. I'd say the same for Denmark, as well, where you're never more than 50 km from the coastline, and the four points that Rick lists under "At a Glance" make a pretty attractive summary.

I wouldn't say "no" to Venice and the Dolomites, or most other suggestion above. I prefer to visit Provence and the French Riviera when it's less hot and crowded/expensive.

3 nights at a destination might not seem enough for mature travellers, but seems to suit the style of younger travellers.
Berlin > Prague > Munich (3 nights in each)
Prague > Vienna > Budapest (3 nights in each)

Vienna's been mentioned several times, and one possible advantage of Austria (in addition to museums and fabulous food & cultural events), is that it lies between the Czech Republic and Venice. Heading west into the Austrian Alps could give you a bit of a break from super-hot temperatures.

Provence and southern France can be quite hot, but that's always a fantastic location, any time of year!