Well you're going in completely the wrong time of year for any aurora borealis, actually it might happen, its just being still white nights season you won't see it. If you go between Sep-May they say you have a good chance of seeing it. I went in April
IIRC and it was rather impressive. Very cold mind.
Iceland is also very expensive, there are few places a Londoner can say that about and Iceland is definitely one of those.
Transport shouldn't be hard, they have a bus system that appears to go everywhere someone would want to go. It is, however expensive.
IcelandAir do some good deals every now and again. I paid £200 pp for a 3night stay in the Hilton and return flights to London over a weekend. It was a fun trip, very relaxing but ended up costing about £300 each for things like bus fairs, jeep rental, drinks, food, cycle hire etc. Also my friend was a space cadet and dressed very inappropriately for the conditions, so I ended up loosing half my base layers to her, 15knott winds and -15°C are harsh. However as everyone has free geothermal heating energy the inside of every building is roasting, with the windows left wide open!