Our basement stinks of cigarettes in our new house

Wash everything thoroughly including the walls. Then open up a bag of cheap charcoal and leave it down there for a week or so.

Place open boxes of baking soda,deactivated charchol,coffee grounds,run dehumidifier,and use Damp Rid

All of the above are good suggestions. If it doesn't all clear up with them, see if you can find where the odor is coming from and concentrate on that area and see if it clears up then, If you get it down to what is left you can always ask for other suggestions. After you get it cleaned up make sure any smokers that come in your new home know smoking isn't welcome in the house and have an area outside for them to enjoy their smoking. We do that in our house at the request of family members that have respiratory issues. We have ashtrays outside our side and back doors, and in the garage for inclement weather.

vinegar is good for neutralizing odors. If it's concrete, mop with a good amount of vinegar and some water. Allow to dry

wash all walls and soft stuff like drapes, upholstery. There is a product usually used for pet stains called odo ban. You might want to try it out I've misted it on tar covered walls and carpet...did a decent job.

Had the same issue in my home. I scrubbed the walls with a vinegar/water mix that I added lavender essential oil to. Worked wonders!

Fabreze and whole cloves