There are any number of things that you might research about shopping centers.  Which you choose will depend somewhat on what your interests are and what data you would be able to collect.

For me, the most interesting studies would have to do with variables that affect how profitable a shopping center is.  I might like to look at whether big shopping centers with many stores are more profitable than smaller ones.  I might like to look at whether a shopping center with a major "big name" store is more profitable than one without.  I might like to look at how many parking spaces (compared to overall floor space) a shopping center needs to have in order to make the most profit.  These sorts of topics would be very important to developers of shopping centers.