Being a response to go ahead i'll listen's request for what they should do and what they should see, as well as not go, do.
Have a compass.
Look up, look down, look both ways when crossing.
Have a little pair of binoculars for when in large cavernous buildings, for peering across rooftops, for seeing what that sign is up the hill.
Leave yourself open to opportunities, such as seeing an enticing door propped open that you might peer into a square, or noticing a flyer for a band that happens to be playing that night, or finding out when the street market takes place, or church recitals.
The things you must or planned to as early in the day as possible, to leave time for: wandering an old town street or river/seaside or if weather doesn't permit to sit in a cafe, bar, covered bench and watch the square and people or read and write.
notable building fronts and sculptures to remember your way back.
Many churches, because there will be some architecture, performance and art that may cause wonder or reflection.
Feel bad about missing stuff. There's always something, and the Mona Lisa is really tiny.
Feel obliged to do something. 'I'm sorry, I'm not interested.' and 'I'm sorry, this makes me uncomfortable/bored, let's try something else.' and 'I'll just hang out right here while you do that, ok?' are all acceptable travelling things to say to a companion. To a member of the public who may be trying to encourage you to donate to something or go to their 'art happening', a more concise 'No, thank you' and walking away will suffice.
Give up too quickly. Often the floor is just one more flight up. Or you actually are on the other side of the street from your goal. Someone may help you with directions and your luggage. Thank them kindly, but not too kindly.
Ignore your feelings, especially when uncomfortable. Backtrack, reorganise, take it easy. Walk away, ask for help, change your plans, compromise.
Get freaked out if you miss a train or bus. An attendant will help you if you ask for it.
Be late for appointments, though.
Worry about being ignorant, obnoxious, noisy, as that is the impression most Europeans have about American Tourists and you won't change their views in one day.
Hesitate to ask about things.
Stress about the language. In a shop you can point at something and use the equivalent greeting and yes or no in that language. It's not a big deal and most people know more words in English than you'll ever learn in theirs.
Rely on just your photos: pick up a postcard for your own memory and momento.
In terms of other practical things:
You might want to pick up an external battery for your phone for quick recharges. you can download maps for offline consulting the night before instead of relying on roaming use. Many places have wi-fi (pronounced wee-fee in several European countries) that you can pop in to dump stuff on to the cloud or check out an opening times or review. (Starbucks always has wi-fi. It's sort of its reason for existing)
Security: keep a copy of travel insurance number(s) and other important contact info in hardcopy on you.
Use common sense regarding belongings. Don't keep a wallet etc in your back pocket: Large currency for the day in one front pocket, smaller currency and coins in the pocket you reach into most. If a situation feels dodgy, walk away.
Money: a coffee in Switzerland might cost you in Swiss Francs the equivalent of 4 dollars, while in Italy in Euro's it may be about a buck and a half, with pastry included. It is what it is.
Allergies: learn the thing you are allergic to in as many languages as possible.
Access: some cities are flat and easy to get around, others all hilly. Old town bits have cobbles: Take care.
Some establishments have no elevators (or lifts), or are hidden away that you should ask where they are. In some cases, a robust mobility is needed, such as the roof of the Sacre Coeur, the whispering gallery in St. Paul's Cathedral. It is often worth the climb.
Winter may be icy, especially overnight: Take care. You can get strap-on cleats for your shows in case of snow.
Some more specific recommendations to see:
Cologne in Germany has a magnificent cathedral and the tour there is well worth it. In i's old town is a Marrionette theatre which i found a little too scary to attend, but you may like it.
Amsterdam is lovely and welcoming and easy to get around and the Rijksmuseum is stupendous. I do recommend the Van Gogh museum nearby it as well if you have any interest in him.
The train down from Amsterdam into Belgium is comfortable and fast. Along the way you may want to consider the following two cities:
Rotterdam is also all of the above with some outstanding architecture, public art, and a charming old town. The museum park there has lots of interest as well.
In Belgium, Bruges is a remarkable city still retaining much of what it was in medieval times, and early Spring is when we visited before: cool, quiet and much to explore. I'll be noding more about it this month, I hope.
In the UK, if you happen to make it up to Edinburgh, former and current E2 Noders include me, heyoka, call and of course Oolong and we love living here. Drop me a line if you are visiting and at the very least you'll get a drink out of it, or a half-day's wander.