Right Bath's nearest airport is Bristol, which is a good 20 minutes away by train n 2 get 2 the train station in bristol from the airport is another 20/30 min bus journey, so ur prob looking at about an hr away from the airport.
Aston's nearest airport is Birmingham, which is 10 min train journey from nearest rail station, which is 2 min taxi or 20 min walk depending on preference.
Edinburgh I'm afraid don't know exact logistics but does have it's own airport.
Social life wise I would have to say that Edinburgh probably has a better reputation but also higher prices. Birmingham has a mix of cheap n expensive, which have different music policies etc. Bath I've not been socialising there but I've heard good things from mates who go there but with my knowledge of Bath I'd probably say you won't drink cheaply there.
For course they are all very good but as someone who does IBAM (International Business and Management) at Aston I can say with doubt it is brilliantly taught n everything links in together, which gives good grounding for business.
So all in all, Aston ticks more of your boxes than the other unis.