My favorite place in Luxembourg is Pétrusse Valley. It is the heart of the city and provides a range of free activities. Starting by Rue d’Anvers, there is a very well-designed outdoor fitness park, fenced soccer/basketball play area, and climbing playground for kids. For anyone looking for an intensive workout, this is the place to go but be warned, the locals are serious (but friendly) about their workouts, so you must show up prepared to sweat!
Heading in the direction of the Grund district, one comes across the spectacular Adolphe Bridge, named for the Grand Duke Adolphe who reigned from 1890 to 1905. This bridge is stunning! The bridge has a cycle/pedestrian bridge suspended just under it (fret not, it is fully enclosed), which provides an excellent platform from which to take in the valley landscape and score some beautiful pictures. This bridge is lit up beautifully every night and during the festive December season serves as a great place from which to view the lights decorating Place de la Constitution.
Lastly, once almost at The Grund in the northeast end, there is the Skatepark Péitruss. It is large and offers skaters many opportunities to test skills. It is busy but users are polite.
Currently, the valley is under construction in an effort to restore the area and allow the Pétrusse river to flow through its natural course. However, pathways are not affected and detours are provided when needed.