Depending upon your city's building code... here there has to be access to
j boxes. So whereever there is a jbox there is a cover. This, as mentioned
by Chris, may be an issue if you wish to finish off the basement later. I
would go with Tim's less is better. Be sure to check on the position for
drilling your holes through your joists. I am not up on these codes but I
think it is something like, no closer than two inches from the floor
upstairs. So no one later nails through and hits your wire, but the center
of the joist is better. That way if you enclose it later you can nail into
the joist from the bottom and not hit the wire either.

What I would have done differently: In my old house I wish I would have
made each improvement on its own circuit instead of connecting up to the
old run. Older homes didn't use power the way we do. If you might use a
coffee urn in the dining room and some other appliance that may draw a lot
you may want to check out what else is on this old circuit. My coffee urn
when hosting lunches can trip my breaker if the other outlets have a
number of items plugged in, like Christmas lights or whatever. Good luck.
______________

KaCe