I'm not in this field, and I know precious little about the conventional methods applied in these situations, but I'm actually going to say mutagenesis analyses seems like the best route. Though a structural approach (eg crystallization) would give a definitive answer, I think it's probably prohibitively time-expensive and of course requires an x-ray source on the chance you're actually able to crystallize.
Mutageneses, on the other hand, are fairly straight-forward though also time-consuming. I can imagine that you could use bioinformatics tools to distinguish different domains of the receptor protein that would be likely to form a binding pocket or something for the ligand, and then you could begin to map the region of interaction by performing a targeted mutagenesis study involving just those likely domains in the receptor ....
You'll need some assay to provide the read-out for ligand-binding to your expressed mutant receptor proteins though -- I've heard of ppl being able to use radio-labelled ligand in competition with unlabelled ligand to determine binding affinities, which in your case would decrease when a mutation disrupts the region of ligand-receptor interaction. I think an analysis of the kinetics of this competition could confirm that the radio-labelled competitor (if it is structurally different than the wild-type ligand) was binding competitively, and therefore at the site of wild-type ligand interaction, rather than at an allosteric site, as a control for the validity of the results.
IF all this worked, then you could begin to figure out which part of the ligand was binding to the receptor by using peptide fragments of your ligand, to determine which domains are capable of binding in isolation.
As I said before though, I really have no idea what's normally done. Haha actually, your best bet would be just to search the literature for current methods
Anyways, good luck!