Were I in your shoes, I’d fly into one of the big airline hub cities such as Munich, Amsterdam, Paris, or Rome. Spend a few days enjoying the arrival city, then take a train to somewhere nearby for a few days then back for the trip home. Note in the following itineraries I’m suggesting taking trains between cities. During the summer the autobahns/autoroutes/autostradas are packed and traffic jams are likely to delay your travel by bus and car. I’m also not suggesting air travel within Europe because the time to get from the city center where most touristy things are to the airport can be extensive, and if you’re flying Ryanair or other budget airlines, the airport may be much farther away, negating any travel time savings. Another train advantage: you’ll arrived relaxed and ready to go.
Sample itinerary: fly into Munich, get a hotel near the main train station, spend two or three days exploring in the old town by foot and local train/bus services, maybe hit Neuschwanstein if seeing the inspiration for The Magic Kingdom is your thing. Take a train (about an hour) to Salzburg for four or five days, using a Salzburg Pass for the sights. Lots of museums, lots of history, friendly people (except the waiters they import from Grouchville for the busiest part of the year), The Sound of Music. Take a bus out to the salt mines or The Eagle’s Nest if they’re on your bucket list. Alternative: take a train to Ljubljana, Slovenia, about 6 hours, for a few days, day trip to Lake Bled, day trip to a waterfall. Back to Munich for a day or two, return home.
Sample itinerary 2: fly into Amsterdam. Spend a few days exploring, taking a hop-on hop-off bus tour the first day to get familiar with where everything is. Use local buses for the rest of the time, eat an overpriced “pancake.” (side note: food is expensive in Amsterdam even at the grocery store, the fruit and veggies are disappointing.) Take a train to Paris for the bulk of your stay. Plan the train travel during the middle of the day as trains from Amsterdam tend to be four hours long and why not be out of the hot sun during the heat of the day? Return to Amsterdam a day or two before you fly out to pick up all the marijuana-themed souvenirs you’ll ever need, return home.
Sample itinerary 3: fly into Rome. Spend three days exploring Rome, staying near the central train station: all local transport ends up there, which is handy as the Rome Pass covers all local transport for three days. Almost all tourist sites are within a 45 minute walk from Rome Termini station, though with the Rome Pass you can use the public transport. The hotel clerk will tell you which to take. Take a train to Venice for a couple days unless you’re really smitten with Venice. Train is about four hours. Alternative: take a train to Florence (90 minutes) for a day or two, then onto Venice (2 hours) for a day or two. Alternative: take a train to Rimini to see the ocean, get passports stamped in San Marino. Return to Rome for remainder of trip. Day trips to Pompeii/Naples and other places from Rome. Return home.
Planning tip: Do not expect everything to be open on Sundays, especially in Germany and Austria. Research opening times for the “must see” places.
Additional planning tip: If squatting is a problem, consider skipping Italy as many bar/restaurant public bathrooms are, ahem, porcelain holes in the ground.