I think the USA would have been a far more logical decision. Without US, UK would have presumably given up anyway, and it's further away.
This is a good example of what the thread was about! The Nazi's had given up on Britain as their only effective tactic, Blitzkrieg, had failed in the sky's against the RAF, the Luftwaffe were meant to clear a path for the heavy vehicles to go in but this island will hold no matter what is thrown at it.
Also In north Africa the Nazi's had been defeated by the British. And in Malta the people held against the constant Italian air attacks and remained loyal to Britain.
Britain would not give up, D-Day was already being planned and Churchill was a very powerful figure who made sure the British people did not give up.
America did contribute greatly, together Britain and USA defeated a lot of Nazi's but the real heroes were the Soviets.