Check the rear under body, suspension and brake lines for rust and corrosion. Check the drive belt condition and the crank pulley for play - the crank pulley is also a vibration damper, so the rubber lamination can deteriorate and separate. During and after running the engine, sniff under the bonnet for petrol fumes. This engine has direct injection, which works at much higher pressures than standard fuel injection. Seals and joints need to be good and age could be a factor.
headlights are a known weakness with this age of Avensis, but they may have been upgraded. A night drive will confirm.
If the car has been regularly maintained and cared well, then some of the items I mentioned, should have been sorted. Oil and filter changes every year regardless of the low mileage is good for the VVTi engine. This engine (1AZ) is totally different to the 1ZZ 1.8 engine which is known to have a high oil consumption. The 2.0l with low mileage should be fine.
Car should have two black remote keys, plus the grey valet key with owners handbook and hopefully key number (for replacement key).
Hopefully this info will help you to decide.