I thought I'd offer some advice for those who got a TT job this time around, and see what other advice other folks can offer. My advice comes from the point of view of someone who teaches at a regional school, in a specific department, so it might not hold for other situations, though I think some of it does, or I wouldn't offer it. (Some of these ideas may be useful for folks adjuncting or doing visiting positions, too.)
If you haven't already, finish your dissertation or thesis. Even if you can't defend over the summer, finish. It did it's job, which was to get you the job, so be done if you possibly can.
Pro tip: If you're like me (and a lot of other people I've talked to), you got to the end of high school and figured you'd learned how to work hard, and then you got to college and realized that you hadn't known what work was. And at the end of college, you figured you'd learned how to work hard, and then started grad school and realized you hadn't known what work was. Becoming an assistant professor seems to feel like that all over again for most people I talk to. It did for me, too. Know it's coming. Having a dissertation to finish on top of everything else is way harder.
Find a place to live that will be as relatively worry-free as you can. Your home is likely going to be a refuge of sorts.
Prepping Classes and Stuff
Contact the IT folks at your school, and find out what sort of course software they use, and also see if you can get access to it a bit early. If you can learn at least the basics before you get to campus, that's often helpful. Or maybe you'll find out that you already know it, and that's one less thing to worry about.
I didn't know when I started that a lot of departments keep past syllabi and such around. In my department, the admin assistants have access to a file for every course. At the minimum (which is sometimes the case), it has the original course paperwork, which outlines what the course is supposed to do and at what level. Sometimes it has other information, too.
If someone at the department level (an admin assistant or a chair) is around during the summer, try calling and seeing if you can get a copy of this information for the courses you'll be teaching right off. You might also be able to get the names and email information for faculty folks who've taught the course recently. (And, if the admin assistant is good, they'll subtly guide you about who to contact because they'll know.)
You should feel free to ask another faculty member for a copy of their syllabus and course information. My guess is that most will happily share. At the very least, you'll get an idea of how much reading faculty might assign at varying levels and so on. If you get a favorable response, feel free to ask about how the course fits in departmental offerings: is it something required? Does it need to prepare students for a specific following course(s)? Does it follow a specific course where students learn X and Y, so you should review those at the start and move quickly to Z? (If you don't get a favorable response from the other faculty member, you can also try asking the department chair these sorts of questions.)
Pro tip: A good administrative assistant is a thing of wonder. Get to know and cherish the people who run things from behind departmental desks and other places.
At schools where I've taught, there's usually a two week or so contract period before classes begin which gets used for meetings. At NWU, the thing starts with university wide meetings, has some college meetings, and departmental meetings. There are meetings for new faculty to get to know each other, and get acquainted with services. Go to these and take them seriously, especially getting to know your fellow faculty members. (At bigger schools, I'm guessing these might get split into colleges, and smaller schools might have fewer new folks, so might combine more.)
Get to Know who to Know
During the week or two of contract prep time, you need to go introduce yourself and start getting to know people at:
The Library. Librarians make the world go around; find out if you should make classroom visits for some of your classes.
The IT Center. Whatever it's called, those people are responsible for making computer stuffs work.
Tutoring Center. Whatever it's called, find out what they can do to help your students.
Research Support. Again, called different things, but invaluable!
Teaching Support. Take advantage of what these folks have to offer, at least a little.
(I'm probably missing some ideas, or there are offices at some places that we don't have, and so on. In some cases, offices will be combined.)
Tenure and Review Stuffs
One of your jobs as a new faculty member is to get ready for the tenure decision. Don't obsess as a first year faculty member, but it's part of your job, so do it.
During these first two weeks, departments at my school are supposed to hold meetings for tenure track folks to give them basic information. This may be led by the chair or by someone from whatever tenuring committee there is. These meetings are really important. Done well, they're invaluable. But try not to panic even if it's not super helpful.
In my department, we have a tenure plan document which lays out in pretty specific ways what we consider in making reappointment and tenure decisions. We give each new faculty member a copy, and go over the relevant parts. We also explain our review process.
Some schools will be more, some less explicit about this stuff. If you can get fairly explicit information, then take it seriously. It's worse, usually, if you can't get explicit information. In that case, you can ask other people who've gone through the process recently to see what they did and ask how it went. This is WAY harder at smaller schools where fewer people go through the process. It's also way harder at schools where TT faculty don't really expect to get tenure.
At any rate, you still need to be aware that there are criteria (more or less explicit) for gaining tenure, and that you need to figure them out and meet or exceed them to get tenure. The good news is that you don't have to do that all in one year. At my school, we pretty much figure that the first year is for teaching and research, and give folks a pass on service stuff as much as we can. In the second year, we add in service and advising.
I was part of a departmental review team this past year for a small department, and we felt that their tenure/review process wasn't clear enough, and recommended some changes. So I know that at my own school, while I feel my department's processes are pretty clear, it's not true in every department. One of the scary things was that the TT faculty all seemed to have different ideas about what was required for tenure, and didn't seem to realize how different their ideas were until our team asked them in a group meeting.
My concern is that if the department or school is small, and has traditionally tenured straight white men, and you're not a straight white man, then you may need to figure out the hidden rules to get tenure. It's not necessarily that the department is hiring people thinking that it's going to use them up and spit them out, but that even a department of folks who try to be decent can unwittingly make things a lot more difficult for people not like them.
Similarly, if you're at a school where there's a desire to move things more towards researching, then the tenure requirements for new faculty may be a lot tougher than for older faculty. Hopefully, schools that do that do so with some awareness and do provide extra support for new faculty research. But if not, then you have to be aware and on top of things if you want to get tenured there. (And you also may have to dance across the minefield of resentment or nastiness from older faculty.)
Pro tip: Make yourself a physical file folder or two. Put your updated CV in there, copies of your syllabi and course assignments. Any time you get a note from a student thanking you for whatever, put a copy in there. When you get any sort of review stuff, put a copy in there.
When you do special stuff (say for a community library or whatever), put the thank you letter in there. (If you don't get a thank you letter, ask for one.) (And if someone does a class visit for you or something special, drop them a thank you note and CC the chair.)
These files will give you the beginnings of your review portfolio and will help you remember all the stuff you need to add to your CV and such.
This sort of thing is on my mind a lot right now because I'll be chairing our department tenure/review committee this year, and I really want to do a good job. So I have a request, too: If you have ideas about what would have helped you succeed as a new faculty member, or what you've seen tenure/review committees do that was absolutely superb (or was horrid), then I'd like to ask for your input and learn from you.
Edited to add: I see to do this every few years. Here's what I had to say way back when (2006).