The thing to remember about your patrol is the grid you're assigned to is completely and totally optional.
You'll get extra renown for it, but you don't
have to even go there. And when you're finished with the 24 hours there, you're free to go as far as your fuel and weapons can take you.
If you check the Reports from your Nagivation officer it'll tell you your currently plotted course and how far you can get on your current speed with your fuel. You can use this to plot a line back to your home port to see how much more fuel distance you have after getting home and that's how far you can roam till you need to go back.
So once you've done your grid, pick somewhere to explore. Follow the convoy lines on your SH3 map to find possible hunting lanes. You can even
download a version of the map you can install in game and see on the nav map when zoomed out.