First, try to take care of any necessary appointments (drs., etc) before you start. Your time at the firm is short - in many cases shorter than in past summers - it will not be viewed favorably if you ask for a day off or half the day to take care of routine things. Of course, if you had an emergency, that would be another thing.
Second (and I know I mentioned this early on in the blog), plan on staying at work all day. What I mean is that you shouldn't ask to leave early for "minor" things such as picking up a friend at the airport, getting to the grocery before your out of town friends arrive, etc. Same point as above, you are at the firm a short time, so put in regular days. You may say this sounds silly, but I and others have had people come to us for these exact reasons and want to leave work early.
Third, check in with the recruiting coordinator and go over start dates, end dates, and first day procedures so you have everything down and there is no confusion. You will likely need identification to establish work eligibility (e.g., social security card/driver's license). Make sure you get them in advance (for instance, going to safe deposit box for ssn card if you don't have it), and bring with you. You want to look organized and attentive.
Fourth, begin assembling your summer work wardrobe if you haven't already. The recruiting coordinator should be able to tell you what the summer dress code is. This is not the time to be creative - you want to look professional and blend into the surroundings. You want people to remember you for your work and professional attitude, not that crazy shirt you wore on casual Friday.
Fifth, if you are spending the summer in a city different from where you usually live, make sure you leave time to get there, get settled, and be ready to leave for work. You don't want to be dealing with "move in" details when you are starting your job.
Sixth, if you have been given an advance calendar of social events, put them on your calendar, so you can block out the times. Social events are important and yes, you are expected to show up. But, let's say your brother is getting married and there is a dinner at a partner's house. Tell the recruiting coordinator or other appropriate person right from the start that you have this conflict. If you develop some working relationship with the partner, it would be fine to mention to him/her that you are sorry you cannot attend but your brother is getting married. Do not blow off social events just because you may not be interesting in [insert activity].
Seventh, make sure you understand who is invited to these social events. If unclear, ask the recruiting coordinator. If guests are not invited, do not ask to bring a guest. Again, should be obvious, but you'd be surprised.
I was going to go to 10, but that will have to wait. I just wanted to get you started as we get closer to summer.