Install and use the app Pocket. I'd often find cool sites and videos using my phone that I figure I would enjoy more if I used the N7 over a stable WIFI connection at home. Pocket works great for saving those links that you can later access on your N7 (or any other device).
Do all your gaming on the N7. The larger screen makes things more enjoyable. And as an added bonus, you'll get much more battery life on your phone.
Most of the time, you'll probably use your N7 in portrait mode. But try going to landscape when using your apps to experiment. For those that are tablet optimized, the landscape mode often offers additional functionality.
Not specific to the N7 or tablets, but you should take advantage of the USB-OTG functionality on the N7. You'll need root access and the app Stickmount.
If you use Google Currents, disable autosync for that app. For a lot of people (myself included), it seems to be the reason for some performance issues.
You'll find that you'll likely use a somewhat different set of apps on the N7 as compared to your phone, though many will be equally useful on both. Some apps just aren't as useful on a tablet, and vice versa. Here are some examples that come to mind.
There's not a big need for fancy photo taking and customization apps on the N7, since it doesn't have a worthy camera. However, you'll probably want to install the basic Camera Nexus 7 app that allows you to activate the front facing camera.
A tablet is better suited to reading and editing documents, so you might consider installing an office productivity suite like Kingsoft Office or OfficeSuite Pro, if you have such a need. Although it's no picnic creating and editing documents on a tablet, I couldn't imagine doing it on a phone.
The new rage is activity tracking apps, to show how far you've run, where you've been, calories burned, etc. This is great on a phone, but kind of useless on the N7.
Watching a movie on a phone is probably not the best viewing experience possible, but on the N7 it's not too bad. So it's probably worth installing a nice media player like BSPlayer or MX Player, instead of using the stock player.
You'll probably also find that most games are more enjoyable on the bigger screen of the N7, so you might consider installing a few more than you have on your phone.
If you don't have a 3G N7, and you plan on using your tablet on the road, you might want to install something like FoxFi to allow tethering to your phone.
Well, you get the idea. In the end, you'll have lots of the same apps on both phone and tablet, but others that are exclusive to one or the other.
I installed about 80% of the apps I use on my phone.
Definitely put anything you use that syncs between devices.
1) Dropbox, Google Drive, any online storage you use.
3) Dropsync to keep folders synced between devices es
4) I use Catch Notes setup to sync to all my devices.
5) Keypass to store all my passwords, set to sync via Dropbox.
6) Mighty Text linked to your phone for texting