Arrive in the capital of Romania, likely in the afternoon. Meet a driver at the airport and transfer to your hotel, the InterContinental Athénée Palace Bucharest. After its recent renovation, this well-located grande dame hotel has become both highly comfortable and attractive. Check into a room overlooking the square and the Romanian Athenaeum concert hall.

Settle in, have a stroll, and consult my list of Bucharest restaurants for dinner. There are numerous appealing choices within easy walking distance of the hotel, including Romanian, French, Italian and Mediterranean options; the concierge will be happy to make a recommendation.

Ideally, take two full days to explore the city, where freshly restored wedding-cake mansions stand side by side with crumbling palaces and soulless communist-era apartment blocks. Simply walking around is utterly fascinating, but hiring a guide is certainly worthwhile.

Explore the Old Town, centered on the pedestrianized Strada Lipscani. It’s full of stylish coffee shops, boutiques in historic buildings and sidewalk cafés. After lunch, tour part of the massive Palace of Parliament, one of the largest buildings in the world.

On your second day, take a private tour of the Spring Palace, the former home of the Ceauşescu family. If you visit one attraction in town, make it this one. Inside are over-the-top neo-baroque salons and bedrooms, a gold-mosaic bath and a massive walk-in closet, still filled with the clothes and shoes of Nicolae and Elena Ceauşescu. It’s an oddly intimate look at the lives of this couple, who ruled Romania with totalitarian impunity until they were executed by firing squad, in 1989.

Also walk around the peaceful and well-preserved Armenian Quarter near your hotel, full of impressive townhouses in various states of restoration, some of which are now occupied by bars, restaurants and shops.

If time permits, also consider visiting the National Museum of Art of Romania and/or the Theodor Aman Museum, both of which are a short walk from the Athénée Palace.

And if you drink, don’t miss the chance to relax in one or more of Bucharest’s atmospheric bars (see recommendations for beer, wine and cocktail bars).

Have a leisurely breakfast at the hotel and perhaps do a little shopping: Turn left out the door and you’ll find My Romanian Store, a wonderful boutique dedicated to Romanian crafts including embroidery, hand-painted Easter eggs and colorful ceramics.

Meet your driver and transfer about 90 minutes south to the Danube, where you board the AmaMagna. This ship is about twice the width of the average European river cruiser, allowing it to offer a large average cabin size, four separate restaurants and a huge sun deck, among other amenities. In this case, bigger is indeed better.

Now is a good time to make your restaurant reservations for the rest of the cruise. Avoid making a booking on top of the Chaîne de Rôtisseurs dinner in the Main Restaurant.

Take the rest of the afternoon to settle in, have a snack and explore the ship. Tonight is the captain’s welcome dinner.

Cruise up the Danube, exploring this strikingly beautiful but lesser-known quarter of Europe. Over the course of the week, depending on what excursions you choose, you can visit dramatic Veliko Tarnovo, capital of the Second Bulgarian Empire; Serbia’s Golubac Fortress, which looks like a set from “Game of Thrones”; lively and pedestrian-friendly Belgrade, where impressive museums and churches stand amid countless hip wine bars and restaurants; Novi Sad, a colorful Serbian university city; and Pécs, a town in Hungary that has obvious Ottoman connections — the church on the main square was originally built as a mosque.

In addition to sightseeing, you can take advantage of more specialized excursions. We visited a winery in Hungary’s idyllic Szekszárd region, for example, touring the cellars and tasting a variety of finely crafted bottlings. In Belgrade, the bicycle tour around the city was quite popular. My favorite excursion was to a Serbian farm, where, together with the owner and her grandson, we made sweet buhtle rolls and lunched on traditional paprika-spiked pasta and freshly pickled cabbage.

On board, besides delicious meals in the various restaurants, you can enjoy a range of fitness classes, high-quality performances by local singers and folk dancers, relaxing in the hot tub, cooling off in the swimming pool and playing a round or two of pickleball.

The ship will arrange a private transfer to your hotel, or your travel advisor can book one in advance. The top luxury property in Budapest remains the peerlessly located Four Seasons Gresham Palace, set in an exquisitely restored art nouveau landmark at the foot of the Széchenyi Chain Bridge on the Pest side of the city (Buda is on the opposite side of the Danube). It’s one of the best Four Seasons properties.

But the Four Seasons now has competition. The Matild Palace, a Luxury Collection Hotel, stands at the foot of the Elisabeth Bridge, in a central Pest location halfway between St. Steven’s Basilica and the Central Market Hall. It has fine views, a proper hammam in the spa, lively bars and restaurants and a historic café. On the other hand, if you’ve been to Budapest before, we highly recommend the chic Kozmo Hotel Suites & Spa in the untouristy Jósefváros neighborhood. Its setting in an inexplicably palatial former telephone exchange building is unique, its accommodations offer impressive space for the money, and its cellar swimming pool is large enough for laps. We loved feeling like a Budapest insider at this hotel.

You’ll have time in the afternoon for some sightseeing. Perhaps take a guided tour of the city’s most impressive landmark, the neo-Gothic Hungarian Parliament Building, followed by a drive up Andrássy to Heroes’ Square. Nearby are two of Budapest’s newest attractions, the strikingly contemporary Museum of Ethnography and House of Music. The panoramic views from the green roof of the former, accessible to the public, are worth the climb.

Budapest can easily fill three more days if you have them, but two would be worthwhile. Take a day to see Castle Hill, including Matthias Church, the Fisherman’s Bastion and the underrated Hungarian National Gallery, filled with masterpieces. The view from its dome is sensational.

The historic downtown area is now fairly touristy but still worth exploring for its wealth of art nouveau architecture and intricately embellished historicist confections.

We also highly recommend the walking tour of Jósefváros that the Kozmo Hotel organized for us; it was a fascinating look into a beautiful but only partially gentrified quarter of Budapest. We also found a Jewish-themed walking tour of the city to be fascinating. A food-themed tour with Taste Hungary would also be well worth your time.

Budapest is richly endowed with atmospheric cafés that rival those in Vienna, plus friendly wine bars pouring startlingly large selections of Hungarian bottlings by the glass. Hungarian wines, both dry and sweet, tend to have great character and personality. The best rank among the greatest in the world.

And the city has several historic thermal baths that merit a visit. Locals got a taste for them during the Ottoman occupation. Széchenyi is the most spectacular, Gellért has a “Grand Budapest Hotel” vibe and Rudas feels plucked straight from old Constantinople. Note that Rudas has separate days for men and women, with only certain times that are coed.

If time permits, stay longer to explore more of Budapest and the surrounding region. Otherwise, transfer to the airport or to your next destination (Vienna would be an ideal choice to follow Budapest).