Aboard a container ship? There isn’t much opportunity for shore leave at all. To be upfront, I never sailed aboard one, but in my present job I spend a lot of time aboard them and from what I have seen you would have enough time to go to Wal Mart, Best Buy, grab a burger at a fast food place and then get back to the ship. Shore leave is becoming more and more difficult in this industry the ships have quicker turn around times, smaller crews, and all the port security insanity has made getting ashore very difficult if not outright impossible at certain terminals.
There are ships that allow for more time ashore mostly bulkers and Government vessels. But, if you get on a tanker or a container ship you aren’t going to see much ashore. You may not realize this, but even though the ship is in port you will most likely still have to stand your watch. So, while you may be able to get ashore it could be at the expense of getting any sleep. I wouldn’t get involved in this industry just for the travel.