The exchange rate at 7-11 is the one set by Visa, MasterCard or whoever else card you got. Your bank might also take a % and/or some other fee, you'll need to check with your bank how much. The maximum limit is the one decided by your bank or 100K JPY, whichever is lower.
This is why I usually change money before the trip, the bank commission and the card fees when you're abroad are usually quite high. In my experience the best rates are with direct currency exchange over the counter.
I'll check the rate and fees with my current bank, maybe I'm wrong.
It depends on what you've planned. For example, if you get a JR pass, you don't need money to get into the city.
I would bring some emergency cash, but there's no way I would plan to exchange the bulk of my money at the very beginning of the trip.
I'll get a 2 week JR pass but I won't activate it right away I think. Or I get a 3 week one, but I have to check if the difference is worth it.
Like I said, I usually change the bulk of my money before going, because CC fees abroad are a killer most of the time. And despite ATMs becoming more common, I've been told several times that cash is still king in Japan.