Hi there, I'm a UK student in the political science/ IR kind of field so maybe I can offer some perspectives!
SOAS is a very well regarded school in the field and puts out a lot of strong research. If you're hoping to apply for PhD at LSE/Oxbridge in the future SOAS would be a good option for you as they all have a lot of links with SOAS - particularly in your chosen field of the Middle East and North Africa. However I can't speak of their international reputation but given their specialism I'm assuming they will only be known by those in the field, which could go either way for you should you apply to US programs later on.
Bath is a solid uni, well regarded for undergrad, but nothing remarkable in terms of postgraduate study.
Queen Mary, on the other hand, from what I've heard is a reputable uni for post grad study. Being part of the University of London will also have huge advantages in terms of name-value when you move back to the US.
I think you're best options are SOAS or QMUL - you'll also benefit from being in the capital which is always a plus for networking (and general fun!)
Congratulations on your offers- its nice to be able to choose between great places! Good luck with your choice.