IsraelRX

I own a 2000 RX300 and my brakes shudder. I know they need changing, but am debating if I should wait for my next service another 1000 miles and do the job at a Lexus dealership, or go to a Toyota, maybe a Japanese specelist shop and do it there hence won't pay as much.

My Q is where to do the replacment, and if Lexus are using better pads or will do a better job?

Lexmex

Compared to OEM pads that I used back in 2002, today´s OEM pads are a step up in my opinion. TunedRX300 can comment about some excellent aftermarket pads that are even better, and that I plan to change to when I switch out to better rotors in the future.

What happens is that your rotors are warped. I have a lead foot so I know this experience. You do not need to take it to Lexus or even Toyota to do this. A brake shop can take off the rotors and machine them. That assumes that you don´t have burn marks, but I doubt it. The machining trims off a teeny amount and if you stick around to watch you can actually see where the warp was after they take 1 or 2 passes on the machine.

A friend of my uncle´s down the street has one of these machines and I now take it to him.

Also consider changing the type of brake fluid that you are using. The Toyota OEM does not cut it at all. I use Ford Heavy Duty (some places it is is known as Motorcraft High Performance) fluid that is low on price and has outstanding boiling point qualities as one example, but others here can tell you about their personal favorites.

TunedRX300

First make sure warped rotors are to blame. Just ask a tire shop to do a tire rotation to swap rear tires with front ones. If the shaking continues, you can replace the rotors at a trusted shop of your choice.
Brake rotor and pads replacement are not hard, especially front ones. I would go to a private shop instead of Lexus. Also ask your mechanic to replace brake fluid (if you have never replace it).
Of course it will be better if you replace both pads and rotors at the same time, but I have replaced front rotors for my Acura w/o changing pads. OEM pads are not bad, just be careful wear indicator is a clip-on, make sure take it off old pads and put on the new ones.
See my signature for better pads and rotors. I have Brembo blank front but should go for Rotora Slotted for better heat dissipation ability and its E-coating for rusting prevention.