If it's got the 3.8 V6 it might not be too bad but the transmissions are not so great on those so pay attention to that. If you're in an area with salted winter roads check underneath for rust. It would be a good idea to have a mechanic take a look at the car. (At a minimum I'd hook up a scan tool to check for codes and maybe check basic data like fuel trim.) If it has not been maintained over those 20 years of grocery-getting it could be on its last legs despite the low mileage. It's a 23-year-old car so it's very likely to need some repairs even if it is basically sound.

If you're really serious about the car, as suggested above you may want to pay a mechanic go over the car for peace of mind.

Even with low miles, a 1999 GM product probably should have all of the hoses/emission connections replaced due to dry rot.

Short frequent trips are probably the equivalent of twice+ the odometer mileage.

I know you need a vehicle right away, but have a little patience and use caution to avoid making an inconvenient situation worse.

Cars like to be used. Short trip use, exclusively, means that the engine did not often get to operating temperature. Ditto for the transmission, as well. That means seals can get hard, corrosion sets in across the systems, etc. How long has it been since the coolant was changed, for example? When were the brakes last flushed? And so forth. 

Any maintenance history? The only antidote to that kind of use is stepped up maintenance, over the years.

At the very least, you should have a thorough pre-purchase inspection done. 

Without a general assessment of the vehicle, all these problems may well come to the fore, sooner rather than later, when used as a daily driver.

I wouldn't even buy it for $1k

YES!