Getting into law school with a foreign Bachelor's degree

I was accepted into some really good international universities (U of Sydney, Trinity Dublin, University of Glasgow), I also got into some good but not excellent universities in the US (like Tulane and University of Texas). Do law schools prefer good American universities over better international ones? Would it hurt my chances of getting into law school if I got my bachelor’s degree abroad?

Short answer is ‘probably not’. The more that the school has some sort of international name recognition (TCD punches above it’s weight there) the better, but also check how many students graduate with first class honors from the program you are applying to. Graduate with a first from TCD, work for a good law firm in the US for a year, get a great LSAT and you should be good for any law school.