The majic number of a car value dropping like a rock is mile 1 off the lot.
As for high mileage car they hold their value better than people expect. For example my dads car which is 11-12 years old and has over 180k miles on it is still worth around 3k and looses relatively little value each year because of its age. Cars min value is their scrap value and as long as it is running it is going to be worth a fair amount more than its scrap value.
I am a fan of keeping cars as long as their repairs do not get insanely costly. My car I had to replace my high pressure line of my AC system but that is because I believe a rock hit it and put a hole in it.
As long as you can trust your car it is worth keeping.
Just save money in the terms of a car payment as a car ages and you just use that extra money for a larger down payment which would really be more than if you traded in your car.
I'm revisiting this thread 15 months later. I kept the car and added 19,000 more miles for a total of 94,000 miles. Maintenance costs for the year, (tires, brake pads, battery), about $500. No mechanical issues. Honda really does engineer a long lasting vehicle. I'm in for another year!