Advice on how to optimize over your offer, or how to prepare for the next stage of your career?
For your offer, you can try emailing other places and let them know you have a ticket clock. They might come forward with their own offers. Try figure out which places dominate, and politely let any job you won't take that your sorry you can't join them. Don't wait until the last second just because (unless you're trying to bridge to another offer, which is risky). Sometimes, if a place is your favorite, and you have no other offers (but you might get more offers), your only negotiating point is your yes. For instance, I will say yes today if you do X, Y, and Z.
After that, enjoy a weekend to celebrate.
After that, meet with your committee to make sure your on the same page for defense.
Then get ready for the move! Moving can be more expensive, and time consuming, especially if you have family. There will be a rush at the end, but try to do some stuff in advance.
Don't go overboard on permanent income hypothesis driven spending! I bought a new car for my wife before I even started my new job, and it was fine, but if could go back, we would have gotten something a little more practical. Even if it makes mathematical sense to pay off student loans slowly, if I could go back I'd pretend I was poor and in grad school to knock them out in 1-2 years.
Also, even if a place doesn't hire you, that doesn't mean that you can't correspond with faculty after flyouts or coauthor together. I visited UC Denver in 2009. They offered Jason Lindo a job (who said no and went to Oregon). They offered Hani Mansour (also from UCSB where I was) a job next. I was next on the list. Hani said yes. I kept in contact with Dan Rees and have coauthored 4 papers with him and counting. And then the next year I went to Oregon to work where Jason Lindo was. Part of going on the market is introducing yourself to the academic world which is both big and small. You can make friends everywhere regardless of where you work.