With a few notable exceptions like cars, petrol and tobacco, most things are more expensive in Luxembourg than in neighbouring countries, there is no way around that. Wages tend to match the cost of living, the minimum wage is the highest in the EU and your salary is also probably higher than what you would get in most other universities (except perhaps Swiss universities, for the same reason). Your income might therefore simply not be as high, relative to the local cost of living, as it might have seemed from abroad.
Accommodation is indeed cheaper in France or Belgium (although not as cheap as you would expect for small towns in this part of the country, as there are tens of thousands of border commuters driving real estate prices up in the whole region) but the commute is probably worse than if you would live somewhere on the outskirts of a large city like London or Paris because public transportation options are limited and the motorway is completely overloaded (especially the A31/A3 from France but also the links with Germany and Belgium).
In Belgium, Arlon is the closest town, in France that would be Thionville and in Germany, Trier. Metz is further away (60 km, one hour to Luxembourg central station by train) but even cheaper and, unlike Thionville, Arlon or even Luxembourg itself, it's beginning to feel like a “real” city (although it's obviously not an international metropolis).
Do note that cross-border commuting brings some complications. For example, depending on your citizenship, arranging a French, Belgian or German visa/residence permit with no local employer could be difficult (but if you don't need a visa, e.g. because you are an EU citizen, that's moot). None of it is unsurmountable and it might not matter all that much for you at the moment but things like unemployment benefits, health insurance, incapacity benefits, child benefits, etc. are also slightly more complicated to deal with.