first i'll tell you about objects that you will be able to see all month, and then give details about events that occur on specific dates in november!
you can still see comet 17p/holmes easily with the naked eye. if you have a pair of binoculars, try using those to see the fuzzy cloud around the central concentration of light, or even the weak tail that has developed over he last couple weeks!! finding the sideways "W" of cassiopeia high in the northeast and looking down to perseus is a good way to find it. it's bright and yellow. here's a finding chart i got from sky and telescope.
the andromeda galaxy is one of the coolest things to see in the sky (in my opinion) because it's the most distant object we can see with our naked eyes... at 3 million light years!! the light you see from it has been traveling for 3 million years to reach your eye! that's cool. it's low in the east at sunset, then rises high overhead as night passes on. it doesnt look like a sharp point of light, rather it's a fuzzy, extended smudge. try to look at it with binoculars or a telescope when you find it!
mars rises during the evening hours, so you should be able to see it after 11pm or so on the eastern horizon as it rises with orion. it will be well overhead by early morning hours when you can also see saturn and venus. you can't miss the amazingly bright planet venus in the morning and you should be able to spot a yellowish saturn above it. continuing upward, you'll see the star regulus (yes, they're still together in the sky, but not quite as close as they were a few weeks ago). still along the ecliptic, and almost overhead, mars shines orange, between gemini, with the bright stars, castor and pollux, and the familiar northern constellation, orion.
MONDAY, NOVEMBER 12: just after sunset look to the southwest to see a bright jupiter close to a waxing crescent moon, as they both sink down toward the horizon. if youre outside early enough and have a good view of the horizon, you'll see the bright star, antares, below jupiter.
SATURDAY, NOVEMBER 17: the leonid meteor shower peaks after midnight. its not very strong, so you might see 10 "shooting stars" per hour if your skies are dark and clear!
the jet propulsion laboratory (JPL) has been posting a couple cool videos each month about various space exploration projects and about what's up each month in the sky! here's whay they point out for the month of november!
you can see fantastic pictures and read more about that blue blob of gas coming off of the star, mira, in a nice post by julianne at cosmic variance.