A advise that I was given is to be "mindful" when I'm not meditating. However, it seems that mindfulness is incompatible with daydreaming (especially those in which we can get really engrossed and lose our sense of the present moment). Therefore, is daydreaming/fantasizing bad?
It is hard to be mindful yet it is beneficial.
SN1.18:2.1: “Few are those constrained by conscience, who live always mindful.
It is easy to daydream yet it is fatal while driving.
Which would you choose moment by moment?
Yes, in general it's a giving of wrong attention.
Whatever a monk keeps pursuing with his thinking & pondering, that becomes the inclination of his awareness. https://www.accesstoinsight.org/tipitaka/mn/mn.019.than.html
Thoughts based on perception of attractiveness, of honor & fame and of sensuality are going to wreck havoc on your training and discipline.
If it's rooted in delusion, aversion or greed then the thought should not be tolerated and is classed as distracting thought.
Removal of distracting thoughts is taught in a likewise named sutta.
In general if one sees these thoughts it's due to lack of development of good perceptions and due to the development of bad perceptions.
If one doesn't even take note of these circumstances then one lacks mindfulness.
If one does take note as one sees the arising, persistence & the cessation of thoughts, feelings and perceptions,then one can make adjustments like ie countering perception of attractiveness by focusing on the unpleasant.
If one can both take note and make the necessary adjustments then one will eventually become quite great;
When, indeed, bhikkhus, evil unskillful thoughts due to reflection on an adventitious object are eliminated, when they disappear, and the mind stands firm, settles down, becomes unified and concentrated just within (his subject of meditation), through his reflection on an object connected with skill, through his pondering on the disadvantages of unskillful thoughts, his endeavoring to be without attentiveness and reflection as regards those thoughts or through his restraining, subduing, and beating down of the evil mind by the good mind with clenched teeth and tongue pressing on the palate, that bhikkhu is called a master of the paths along which thoughts travel. The thought he wants to think, that, he thinks; the thought he does not want to think, that, he does not think. He has cut down craving, removed the fetter, rightly mastered pride, and made an end of suffering."https://www.accesstoinsight.org/lib/authors/soma/wheel021.html#ch-1