What is the correct inflation pressure for hybrid road/city bike? I have a road bike and I got a flat tire probably after going back on the road from the sidewalk very carefully. I guess I pinched my tire. 

I usually inflate my tires to 7 bars. Is it enough and can I avoid this kind of issues with a higher pressure?

I also discover that I can replace my tires with some with Kevlar on it. Is it a good alternative?
When you take the tire off to fix the puncture- find where the hole(s) are. If there are 2 holes approx the rim width apart, then you have a pinch flat. If it is just one hole, then its probably glass/thorn etc. You will get punctures from glass/thorn no matter what pressure you run at.

Once you have checked, if it's a double hole- run your pressures higher, suggest you look at your tyre and run just below the max (eg. if max is 100 psi (7 bar), run at 90 (6.2 bar). If you run them at the max pressure, it can feel very "hard" on the road (but is used for maximum efficiency) 

If it's a single hole- then looking at tyres with Kevlar/other puncture protection would be a good idea (especially if it continues to happen).