Luxembourg is forgotten by most European travelers, though it really shouldn’t be. It’s loaded with history and its placement on the crest of a mountain group makes for some amazing views to go along with endless charm.
This city is often discussed when those lists of richest countries per capita come out, and many in Luxembourg are very wealthy, but that doesn’t really translate into the tourist scene, so prices are moderate and typical of this part of Europe.
Being a smaller city there are fewer budget options, including only one proper hostel, but there are enough cheaper hotels in Luxembourg to meet the demand most of the year. You can see pretty much all the highlights in two days and one night, so even if you can’t find a cheap hotel it won’t impact you much.