I have two old bikes. Without changing their rims, I want to make them city bikes which I will use for going to work. I prefer thin tires as much as possible. Could you help me to choose a good pair of tires, please?
You are fortunate because both bikes have very common tyre sizes and you will be able to choose from a variety of tyre models from all the top manufacturers. As stated, a "daily use" tyre benefits form being a bit stouter and will mention puncture resistance and potential lifespan in the marketing literature.
Suitable 26" tyres are available from about 1.5" wide up to 2" wide which should all work no problem with your existing rims.
Suitable 622 (700c) tyres are available from 28 to 40mm wide which should fit your rim but you will have to be careful with frame clearance if you choose a wider tyre than the 35mm currently on your bike. Robust tyres are available even in sizes as narrow as 23 (which may not be suitable for your bike) as these are frequently used by cycle messengers.
A broader range of sizes is available but may require different rims and/or frame clearance than you currently have and also have less availability in the general purpose category.
As this site does not do shopping recommendations I will refrain from doing that, and will answer what makes a good city tire.
A good city tire is one that is robust. It will ideally have good puncture resistance and last a long time (c.f. race tires where weight and grip are more important). It will be large enough size wise to be able to absorb bumps and hitting obstacles. This larger size improves puncture resistance, adds comfort, and requires less pumping up due to both lower pressure and higher volume meaning air escaping from the tube has less effect on tire pressure.
The best tire for city bikes will be completely smooth, or small tread, depending on the quality and types of roads and cycle ways it will be used on.
For most people a city tire needs to be economical - not necessarily cheap, but good value over its expected life (c.f. a race tire which may cost the same but is not designed to last as long).
Generally weight is not considered a major issue for a city tire. While lighter will be better, durability is more important and to maintain durability while saving weight means the tire costs a lot more.
Your desire for thin tires is the exact opposite of what makes a good city tire. (To me, thin would be less than 25mm or 1"). The 1.5"+ (which you have) make perfect city tires.