Please don't confuse anticoagulation testing with blood glucose monitoring. What you eat, and when you eat it, won't have immediate effects on your INR like they would for a blood glucose test. (What you eat matters -- if you eat a lot of green, leafy vegetables that are full of Vitamin K, you may see some effects within days or perhaps sooner).
Coumadin is slow acting, and slow to leave the system.
Personally, I take my coumadin before bedtime. It's just the habit that I've gotten into. I don't see much difference whether I take it at 10 PM or at 1 AM (although I try to keep it at around 10 PM).
I've tested at end of day (sometimes around 11 PM, mid-day (3 PM or so), and early morning) and I don't think it really matters. INR testing isn't like blood glucose monitoring, and I don't think there are INR 'swings' regardless of when you test, or when you take your coumadin--although it's probably best to take your coumadin pretty much the same time each day.
I got the feeling, from the way you asked your question, that you may be doing a LOT of testing - as you would if you were testing for blood glucose. There are other threads on this forum discussing this. Once your INR is stabilized, you may only have to test once or twice a month - this depends on a few things - if you are using a service, like Alere, you may be asked to test and report results weekly; your MD may want tests every 2 or 3 weeks, etc. If you have an abnormally high or low reading, you may have to make a small change to your dose and test a few days later. In NO case I can think of (other than heparin prescribed by a doctor, or something, that causes rapid changes) will testing two or three (or more) times a day be of any more value than just a single test.