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Quite alright.... No there is no cost to go ashore when docked. The only places I that should be avoided for a stroll that I can think of are St Petersburg, where the docks are miles from the city and you need a visa, some ports in Jamaica which can be dangerous if you leave the port complex and La Guaira in Venezuela where, although we did walk the town, we felt extremely unsafe after a while and it is awful anyway. It is always a good thing to be street-wise anyway, believe it or not Nassau, Acapulco and Panama can be very dodgy just off the main streets. If you could be more specific about which area or ports that would be helpful next time ..... Neil.
No you just go off and on as many times as you like.
In general no you do not pay to do your own thing with the exception of Russia there you will need a visa.
Sometimes the ship docks in rather unpleasant surroundings and a short distance aways from the sights and towns etc, usually the cruise line will put on a shuttle bus to to best areas, usually are free or at very small cost.
No it's not a silly question ...you are free to come and go as you please at no additional cost. You can research the ports of call in advance, and indeed if you call your cruise liner customer care, they will advise you on how close the ship will be berthed to main city/town/sights etc. and whether easy or difficult to manage on your own. If you are independent and do your research you can manage most ports of call generally with ease. Just make sure you are back on board well in advance. We always allow an hour.
Don't give the cruise lines any more ideas to take money off us !!!!!!!!!