At Zeebrugge there are two very obvious choices. Catch a train or taxi for the 10 mile journey inland to Brugge, also spelt Bruges or Brugges. The rail station is very close to the historic centre, and its easy to explore on foot. Compact centre, canals, cobbled streets, fine architecture including merchants' houses & almshouses, brewery tours, canal trips (but small open boats, no weather protection).
Or from Zeebrugge catch the Kusttram, a tram which runs the entire 44-mile length of Belgium's seafront. First part to Ostend doesn't give you views because it runs behind sand-dunes, beyond Ostend it mainly runs along the seafront. At the end of the line, near the french border, is the resort of De Panne (seafront prom, small but interesting town centre). Interesting WW1 and WW2 Atlantic Wall remains/museum just west of Ostend, not well-signed so ask driver to tell you where to get off, worth mebbe an hour & half but a fair walk from the stop to the museum. Definately stop off at Ostend - also compact , no architecture of note but very pleasant & laid-back and a lazy stroll between harbour, beach, seafront, & pedestrianised centre. Tram costs only about 7 euros for the day (but buy your ticket from kiosk or shop near the stop before you board, driver doesn't handle fares). Trams every 10 mins or so, hop on/ hop off. Amsterdam - If your ship docks at the cruise terminal, by the rail station, then the centre is easily explored on foot. Must-do's are a canal cruise - large vessels, fully equipped, commentary in english (poss amongst others), very professional. And the red-light district - any time of the day, and with your lady on your arm, it really is the done thing. The Rijksmuseum (old masters paintings etc) is only partially open due to building work, and you'll need to take a bus or taxi. The Anne Frank House is a bit of a walk and has a dreadful reputation for long long queues and anticlimax, so unless you have a particular desire best to give it a miss. Cherbourg - sorry, can't help. Mr Google can fill in most of the detail. Have a good one, Chris.
Nice one Chris and so accurate. I would add that in Cherbourg one thing you can do is to rent or hire a car and go to see the Normandy D Day beaches, or around to Bayeux for coastline and the tapestries, or again the west coast and enjoy the fruits des mer and a glass of calvados. You can get taxis or mini-cabs for the day but they are a tad expensive in France. Le-Mont-Saint-Michel is about 100 miles away so a long day trip but a good one. ....... Neil.
I really must amplify Neil's recommendation and visit the Normandy beaches. A hire car will make this much more interesting than a ships tour. Cherbourg itself doesn't offer much. An early start will get you to Pegasus Bridge near Caen or, if you do not wish to drive so far, St Laurent (Omaha Beach) or St Mer Eglise and Grandcamp Maisy are easily done in a day. A Michelin road map of Normandy will be useful to take with you. Avranches and the D day museum there is also a must.
Good thinkin' Neil, ust admit I didnt mention Cherbourg cos by all accounts there's b-all there. But yes, American D-day beaches start at Utah Beach only 25 miles from Cherbourg. Good airborne museum at Ste Mere-Eglise, good museum on Utah Beach near Ste Marie-du-Mont. & remains at Pointe Du Hoc. Several large, impressive & immaculate cemetaries. British/Canadian beaches start 60 miles from Cherbourg at Arromanches, (Mulberry Harbour remains, museum ok but not brilliant) through to Pegasus Bridge (super museum/sights) between Caen & Ouistreham, but now you'e 80 miles from Cherbourg. Xpensive museum in Caen. Caen & Bayeux have their traffic problems, coastal roads are country lanes, but usually uncluttered. Good fast road to Mont-Saint-Michel. Dial some of these names into Google for full details. Chris.
Further to Neal's answer about Zeebrugge I expect that Cunard will lay on shuttle buses from the quayside. The bus drops you close to the railway station at Blankenberge about 5 miles away. Return fare to Bruges is 5 Euros each, much cheaper than going on the shore excursion trip. Blankenberge itself is a nice seaside town with a delightful Promenade and sandy beach.