No one knows your car better than you and your mechanic; if you used a non-dealer to service your car. The ES 350 and Camrys are built to go well into 300K miles. Here is the deal, given the condition of the car - and if its cosmetically acceptable to you, I'd keep it - sweat the asset till its dead or you don't want to use it for cosmetic reasons.
A new car will cost you a few hundred dollars a month for the next 5 years, if you purchase it and get a 0% or low interest loan. Or pay $ 40K+ out of your pocket OR cough up a few thousand down payment and a few hundred each month if you lease.
Even if you spent $ 2K over the next 24 months by keeping the car, you are still saving a LOT of money. I would keep the car with the proviso that its in decent mechanical and cosmetic condition.
Another thing to consider, the Internet of Things - IoT - is imminent over the next few years; the longer you wait for your new car, the better technologically advanced car you will get. Lane departure warning, collision prevention, broadband connected car with direct google maps etc. etc. will be commonplace before we know it.
Of course if you have money to spare and can afford to change the car every few years, that's a different story :-)
FWIW, I don't drive much. I sold my leased MDX 2/3s of the way through the lease and made money in selling process, saved $ 7K in lease payments. Net-net, saved $ 10K and got an '07 Camry in like-new condition with 54K miles.
Good luck and happy, safe driving!