Luxembourg has been a fortress city since the 10th century and since the middle ages has played a strategic role in many European wars. The city actually has a huge network of tunnels that run underneath that you can explore (look out for signs for the casemates or ask at the tourist office). Have a look at this site for another overview of Luxembourg.
You can generally get around in Luxembourg only speaking English. Occasionally you might need to speak French. You can pretty much choose which language to converse in - many Luxembourgers will speak French, German, English, their native Luxembourgish and another couple of European languages for good measure.
Nittel to Luxembourg City - 32km
Luxembourg to Trier - 50km
The Old Town is the heart of Luxembourg. Walking around you'll find great views over the city walls as well as quiet, narrow streets and open squares. There's no one thing to see - the views from all the sides of the city are impressive.
On the Marché-aux-Poissons this modern museum is an enjoyable place to visit. The visting exhibitions can be very good, the fixed exhibitions are still interesting. The museum is close to the Duke's palace.
The Duke's palace is right in the old town on rue du Marché-aux-Herbes. It's really just a semi-detached, with restaurants right opposite. As you pass make sure you pause to enjoy the curious marching of the Luxembourgish sentries.
Along with Neumünster Abbey and the National Museum of Natural History the area at the bottom of the fortress walls known as The Grund has a lot of nightlife. Bars and restaurants are easy to find.
Once you descend into the Grund you can enter the park that surrounds the city. You can walk pretty much all the way around the city so it's a good way to get an overview of Luxembourg.
Or MUDAM as it is known. This is a new museum just off Kirchberg. The building designed by the Chinese architect Pei is very interesting - probably more worth seeing than the collection inside, though there are usually a few interesting pieces. The building makes a visit very worthwhile. Furthermore it's right next to the Philharmonie, so you can visit it before a concert.
This shell shaped building has concerts most days. The main hall has an impressive acoustic. If you fancy an evening out you can find concert information through their site and book tickets online.
If you want to do some window shopping then Luxembourg is fun. The shops tend to be of the Louis Vuitton-Hermés-Dior variety. They are expensive. That is because most people who live in Luxembourg city are rich.
If you find the main tourist office then you're in the middle of the old town which is where the shopping is. Shops stay open until 6pm normally. In general nothing is open on Sundays.
If you want a guide or detailed shopping information then Ines is still your woman.
Utopolis on Kirchberg is a cinema complex that plays films in original language versions. So if you're a monoglot and want to go to the cinema, you can.
Booking is essential at all the following restaurants. these are just a few we like. Luxembourg has the highest concentration of Michelin starred chefs on the planet. Have a browse on the Internet - you're sure to find some interesting places.
For breakfast try the Table du Pain in the old town at 19, Avenue Monterey.