I personally like any time in the second half of the month. The reason s that at closing, you are prepaying interest for the remainder of the month and your first mortgage payment will not be due until the first of the following month. This gives buyers a good "relief valve" after getting through the purchase, moving, etc. If you close on the 10th, for example, you will have a payment due in 3 weeks.
In the end, it doesn't really matter what time of the month, as we prorate expenses such as taxes on a daily basis. If you wait too close to the end of the month, you'll be stressed out with all of the stuff going on with the attorneys involved. Try to avoid the last day.