Definitely Friday.

The park should be pretty much desserted on a Friday in Oct. Yes, the park does close early due to Knott's Halloween Haunt. Some rides won't be open because of KHH and some rides will have things covered up that are decorations for KHH. Last year though all the added spiders to the Calico Mine Train were uncovered. Only the bloody and maimed bodies were covered.

Ditto on Log Ride.
Get there when it opens (10 a.m.?) and you'll be able to ride all the rides you want, at least once, probably more. When it's uncrowded sometimes you can ride the rides without getting off. If you are a coaster fan definitely ride Xcelerator, Montezumas, Jaguar, Silver Bullet, and Sidewinder. I think Ghost Rider is too rough as is Boomerang. Also pretty good are Pony Express some of the other carnival type rides. And don't forget to ride nostalgic rides as well-The train and the Log Ride. Stage Coach won't be open due to KHH.
If you have small ones they'll love Camp Snoopy.
Don't forget to have some of Mrs. Knott's Famous Fried Chicken. We usually get it from the take-out located just next the Chicken House and get our chicken, mashed potatoes, and biscuits there. It's from the same kitchen, and it's less $$. If you do get it to-go, be sure to ask for the chicken hot from the kitchen. They have no problem doing this (an employee told us this a few years back after returning some barely warm chicken). There a tables not too far from the to-go, located near the entrance. Of course, if the weather is bad, eat at the restaurant.
Have fun, I love Knott's for what it is-it's not Disney, but it's still great fun and weekdays are a perfect time to go.
Oh, and for dinner there's a Claim Jumper restaurant across the street-great food, huge servings as well as a Fat Burger just down the street.