Like Olive said, where you're flying from dictates what sort of choice you have - if you're flying from the East Coast but not flying out of New England, you probably won't have any choice but to take a red-eye! For example, the only three direct flights to the UK from Atlanta (BA and Delta, to Gatwick and Manchester) all leave after 6pm.
Another thing to consider is what sort of travel you're facing on the other end. I live in the North East of England, so even if take a red-eye into London, I won't get home to Redcar until late afternoon. It's easier to budget in that extra day for travelling, try to catch a nap on the plane the first night, stay up all day and go to bed at a reasonable hour the second night - I find that when I plan things this way I'm rarely jet-lagged upon my return to the UK. Flying to the US is another barrel of monkeys entirely!