hi, I was wondering, when would be the best time to approach a table for the first time? right after they order their drinks or after they order their meals?

The ideal time is after they order their drinks. If you can't get them after the drink order then come just as they are about to finish (not while they are actually finished).

Nowadays, I perform at the Hilton hotel's brunch so there isn't an ideal time and I go up while they are eating. It doesn't bother people as much as I thought.

Do you mean approach or perform?
Because I've been asked to perform right after they ordered their drinks but every 2 minutes or so the waiter came with menus/take their order and it interfered with my routine.

I meant to perform after they take their order. But you should also be talking with the staff so they know not to interrupt you.

1. See a main meal on a table don't interupt them
2. If you see menus on the table once again don't bother means they are ordering

Best time to approach the table once they have ordered but have not recieved there meals yet.
Just approach them and ask them if they would like to see some magic while they wait for there main meals and they will never refuse because you have given them a practical reason to be there.

Another time to approach is to entertain them when they have just finished dinner although don't entertain them too late the restaurant still wants to turn over tables.

If your in the middle of a performance and the crowd seems friendly and inviting, it's sometimes a good idea to plant something like a force card in a harder to reach location like under the table, under a candle, or if your ballsy enough...in a spectators shirt while you reach over and shake another audience members hand.

After they're finished their dinner you can give your audience the much needed excitement they so sorely missed between the apricot chicken and wondering if you would ever come back to show them just one more thing.

After you reveal the forced card in such an impossible place they will no doubt kneel before you and praise your astonishing ability (hopefully with a $5 note)
Now I've only tried this a few times, but each time was a success of phenomenal reactions

That is a great idea! Thanks!