what else to check??

I've had my '99 LTZ for about three weeks now. The only obvious thing that I knew needing changing was the antifreeze: DOne. The oil and tranny fluid look good. Brakes seem to be working fine. Tires are new, belts look good. Is there anything else that I should do/check, having just bought the car recently? There don't seem to be any problems, I just want to make sure that all necessary maintenece is done to try to avoid problems in the future.

You have a seven-year-old vehicle, with unknown mileage. Unless you have reliable service records indicating otherwise, you really should perform all the scheduled maintenance require for a vehicle of that age and mileage. That doesn't necessarily require replacement of a lot of components, but will require a lot of checking: The cooling system service is a good start; Wheel bearings are essentially non-serviceable items, so you can forget about that; Removing the wheels and inspecting the brakes would be a good idea; While the wheels are off, check for CV joint lash and boot leakage; Inspect the exhaust system integrity; Check the lower control arm bushing condition, and upper strut mount bushings on all four corners; Inspect the rear trailing arm and lateral link bushings; Check the half shaft seal at the transaxle case, and check for play in the steering rack; Change the transmission oil and filter. There is no real need to "flush" the transmission, but changing the filter and at least four quarts of the oil will be a good start; Unless you know what oil was used in the engine, and know that it is the type you want to use (or you don't care), change the oil and install a good filter. The term "good filter" usually excludes anything painted orange, or any variants from the Allied Signal group. Use a Wix, Hastings, AC, or Champ filter; Check all the lighting and repair as necessary; Replace the fuel filter; Inspect the air filter and replace if necessary; Clean the throttle body and IAC; Remove and clean the PCV valve. Inspect the PCV hose for damage and obstruction. Inspect the fresh sir (CCV) hose for accumulation of sludge and damage; Inspect the accessory belt and tensioner; Check or replace the spark plugs and inspect and resistance test the secondary ignition wiring; Rotate the tires and set tire pressures (including the spare); Check or replace wiper blades.
That should cover the basic mechanical service required for an older vehicle. I may have omitted a few things, so feel free to correct me where I may have overlooked something.

If it were mine, I'd also perform a complete body and chassis lubrication. The owner's manual makes a brief reference to this as part of annual maintenance, but doesn't detail it as well as the service manuals. The factory service manual outlines all the points to be addressed. I would suggest: Clean grease fittings on lower ball joints and pump fresh grease through as necessary. To my knowledge, there are no other grease fittings on OEM parts for a '99, but if you discover them (probably replacement components), treat them the same; Lubricate body mount and suspension bushings with silicone oil or an approved rubber preservative; Clean accumulated dust and dirty deposits from hinges and latches, then lubricate with ISO 68 oil (SAE 20) and NOT any kind of spray lubricant. Lubrication points include the door, hood, and deck hinges, door, hood, and trunk latches, door detent rollers and springs, wiper linkages, service and parking brake pedal pivots, shift linkages, fuel filler door, steering shaft joints, trunk lid springs, and hood lift strut attachment points; Clean door, window, hood, and trunk weatherstripping and apply a thin film of clean silicone grease (such as dielectric tune-up grease) to each of them, rubbing into and around the seal surfaces; Clean and lubricate the exposed ends of park brake cables and wipe with a thin layer of white lithium grease (Lubriplate 107 or equivalent). Work the cables through several cycles to distribute the grease and wipe off any excess; Lubricate seat adjustment tracks and tilt controls with white lithium grease and operate the controls to distribute the grease; Lubricate all lock cylinders with powdered graphite (Panef Mfg. offers a white graphite which is non-staining).
That should keep you busy for a few hours, and should reveal any serious problems you may have with the vehicle.

wow. I can see you know your stuff! I thought a '99 was new! You must remember my other vehicle is a '93. I'll probably just print your maintenence list and take it to my mechanic and see what he wants to do. I don't have the skill or nohow to perform many of the above named tasks. I'll probably do the lubing of the doors, hinges, etc. myself but I would feel more comfortable letting the "expert" handle most of them. Thanks a lot for the great information. You are awesome!!!

Those are all relatively low-skill tasks. It's just routine maintenance which should be performed on almost any vehicle. Assuming the vehicle was equipped with a lug wrench and jack, you should be able to remove a wheel one at a time to inspect brakes and suspension components. It would be better to have a floor jack and at least two jack stands, and you NEVER want to get under anything on a vehicle resting only on the factory jack, or anything not supported by adequate jack stands.

Still, with minimal tools, equipment, and skills you should be able to complete the majority of the maintenance and inspection without having to pay someone shop rates to perform menial labor. About the only tasks which might require lifting the vehicle are the brake inspection and some parts of the suspension inspection - I've gone back and highlighted those in Red. The park brake cables and even the fuel filter can be accessed without raising the vehicle, but it does make it easier.

The cleaning of the PCV, IAC, and throttle body will only require removing a few pieces of the air intake ductwork and air filter lid. You'll have to remove the lid to check the air filter anyway, so all that's left is removing the other end of the intake hose at the throttle body.