In game there are no "level zones" marked on any maps. However, you can search "Black desert online leveling guide" and this will show optimal areas for leveling up in (there are quite a few so choose one you prefer, I haven't use any of these so I cannot vouch for their credibility but there are guides for Level 1 to 50 in 15 hours which I have seen people complete)
You can tell a monsters level by looking at the colour of their name. The colours are very similar when the mobs are below your level so it isn't easy to tell at a glance, but lower level mobs have a green name and higher level mobs have a red name. Grey names mean 5 levels below you, and purple names mean 5 level above you (don't try to fight these unless you have good gear and high accuracy).
At 4 levels below you mobs will have a very pale green tinge to their name. 1 level below you they will have a very bright green to their name. At your level they have a white name. 1 level above you it will be a light red tinge to the name moving to a a bright red at 4 levels above you.