You can't just slap down new concrete. It will never bond. Some options:
1) They make bonding agents for this. Not sure how well they work.
2) vinyl patching compound. Probably your best bet for damages stairs. Not as good as new concrete, but might hold you over for a while.
3) Epoxy. probably the best for small repairs. I use it quite a bit for small cracks and pits.
Without seeing pictures, I'm guessing #2 is maybe what you want to try first.
With out any design sketch, a good way to bond wood to concrete is using threaded anchors
or threaded inserts
The difficult part is placing these inside the concrete column, to be level and not get dirty from concrete.
![enter image description here](https://i.stack.imgur.com/rrvhj.jpg)
So using a fairly large size, so its easier to clean later, and easier to screw into.
Basically you would then insert a metal shaft in the wooden part and use a long screw that goes throught the wooden shaft freely but its head will clam the shaft.. and when you screw it into the concrete threaded anchor you essentially pull the wood tightly to the concrete pillar..
I could not find a diagram that illustrates this but this picture depicts the concept
![enter image description here](https://i.stack.imgur.com/MBZCd.jpg)
So imagine the top of the screw, the part of your wooden table.. and the bottom part the concrete pillar, but using the threaded insert, instead of that bolt in the picture.
I have seen this used in building public park benches, with wooden planks fastened to concrete pillars... it is highly durable and very vandal proof.
But you might consider putting in three studs per column.. Three, in a triangle shape.. as this helps stabilize heavy objects. Or four in a SQUARE shape.. Using 1 you will need some sort of cross member or brace.. 2 is almost useless as you still need cross members or braces.
Best Answer
A machine screw anchor is a good option for repeated removals and reinstallations. They're also available in standard thread sizes, so they can accept machine screws, eye bolts, or hook bolts. The downside is that you'll have to buy an inexpensive but specialized setting tool for each size of bolt you want to install.
The installation process is much like that of the lag shield below, except that you'll have to use the setting tool (third step) to seat the machine screw anchor into the hole.
Image Source
A lag shield anchor may be another acceptable option, but it is not as "reusable" as a machine screw anchor. It creates a sleeve inside the hole in your concrete with threads for a lag screw to grab onto. When the lag screw is inserted, it expands the shield inside the hole.
The installation process:
The lag screw will still be removable, but keep in mind that many repeated removals and installs may eventually weaken the anchor.
Image Source
(I have no affiliation with either distributor, they just had good illustrations.)