OP's question brought an old XO post to mind...
Based on your reaction to getting the offer, this is probably the best thing that could have ever happened to you. I encourage you to enjoy the summer and take accept their offer as nothing in the world will cure you of your prestige obsession quicker than some time at S&C.
During orientation, they'll give you an S&C shoulderbag and you'll wear it with the S&C logo facing outward so any other commuters in the know can see it and you'll just know that they're either impressed or envious. And that will make you happy and proud. And then you'll try to figure out the best way to ensure that you're sworn in as soon as possible after receiving your bar results because then you'll get the box full of business cards that say "Sullivan & Cromwell LLP" with your actual name underneath. You'll be giddy at the thought of casually passing one (mid-conversation) to some acquaintance from undergrad you've lost touch with.
You'll start working and you'll notice that there are an awful lot of "Farewell" emails and someone will tell you that the farewell emails can only contain 4 names at a time per firm policy because the partners decided sometime in 2004 that emails indicating 6 or 7 people were leaving the firm in a two week period might cause some unhelpful whispering. You'll talk to a midlevel associate who is super-psyched to work at S&C and you'll find out that he (not a lot of shes) lateralled from some firm that frankly you would never have considered working for (too TTT for you). When you get back to your office, this will trouble you a bit, you'll wonder if your own escutcheon is being blemished by the presence of this type of person (i.e., non-elite) at your S&C. But that feeling will pass as you'll find plenty of other like-minded first years who equally relish the prestige as you you head for a drink at Ulysses (shoulderbag logo facing outward).
Then you'll get staffed on your first big deal and you'll work late night after late night and then on the weekend and on to the next weekend and then on to the weekend when you had planned to go to a friend's wedding. And you won't go because the work has to get done and you have dues to pay (or so you'll be told). You'll get a little bit upset about this turn of events, but the arrival of those business cards will soften the blow.
You'll meet more and more laterals from firms that you would never work for (some you've never even heard of). You'll note in the farewell emails that some of the junior and midlevel associates leaving S&C are going to those very same firms. Survival of the fittest you'll say. But late at night, when the air conditioning clicks down from a barely perceptible hissing sound to complete silence, these things will bother you. But you'll tell yourself you're just tired and frustrated and anyway you have work to do.
You'll have lunch with Rodge and he'll tell you that business is good and that he's listening to associates' concerns about quality of life issues. You'll notice that some of the senior associates visibly roll their eyes at each other when this comes up, but you won't mind that much because, really, what other firm's managing partner regulalry has lunch with associates to hear their concerns (and takes notes!)
A few months will pass, a few marathon deals will happen, you'll have to re-schedule a vacation but you'll tell yourself that that is to be expected.
About a year in, a couple of your classmates will crack and start talking about how much the job sucks. They'll very likely have gone to Yale Law School. You'll joke that they couldn't hack it when they leave the firm for a clerkship, or an academic position or to go to a firm in another city.
Things will go on in this pattern and you'll notice the fact that you're working a lot harder than your friends who went to "peer" firms. At first you'll be proud of this and brag about it, but after a while you'll find yourself downplaying it. At least when you have the time to get out and socialize with your law school friends.
Something will happen: a partner will scream at you, a senior associate gunning for partner will blame you for her mistake, the partner will tell you that the trip to Europe your spouse meticulously planned just won't be able to happen (he'll be really sorry and will tell you a funny story about the exotic vacation he missed or cut short). Doesn't matter what, but you'll get really pissed and you'll start to take some of the 4 or 5 calls from headhunters that you'll receive every day at that point (vultures spell blood). They'll give you the names of firms that you laughed on in the days when you posted on the XOXO board, but you'll find yourself looking into them. The headhunter will encourage to just listen to their offer and you'll consider doing so. But you won't leave because then you'd have to give up your business cards. And stop wearing the shoulder bag. And the bonus is only x months away so you'll start thinking about it then.
Until one day you won't be able to take it any more and you'll find yourself arranging to meet with people from a lightly regarded firm for a position in their New York office. And you'll worry that the XOXO crowd will see you.
And you don't believe any of this will happen, but I suggest you print this out and keep it in the top desk of your drawer so late at night when you're feeling sorry for yourself, you can add to the list of reasons to be miserable this fact: someone told you this was going to happen and you thought that person was crazy.