It seems like you're supposed to do the dishes, drive your car, etc. and always be mindful of the present moment, but when is it okay to think about something like a work project or a hobby or something besides the moment? Even when you're meditating you're supposed to not be thinking... It feels like the only time you're allowed to think about things is when you're sitting alone in a dark room.
"In the original Mindfulness Sutra, The Buddha described what he called the Four Foundations of Mindfulness. These teachings remind us to be aware of our bodies; aware of our feelings and emotions; aware of our thoughts; and aware of events, as they occur, moment by moment." Lama Surya Das, Awakening the Buddha From Within, pg 301-302. (Italics are mine.)
Obviously, mindfulness does not mean that we should not think, rather that we do not dwell on the past, and stay in the present moment. If the present moment means that you need to think about future plans, that is acceptable. Just realize that those future plans are not set in stone, are subject to change, and will be in the present moment when they are implemented in the future.
As for meditation, it sounds like you are describing Samatha, or Calm Abiding Meditation. This does indeed call for training the mind to not have as many conceptual thoughts during the meditation. If one arises, we are aware, and dismiss the thought by returning to the object of focus, such as mindful breathing. The following link may be of assistance to you.
We all know what thinking is. I would like to add this instruction on mindfulness by Bhikkhu Bohdi on an online lecture.
Mindfulness "functions in an atmosphere of detachment...[and] aspires toward a pure objectivity, an awareness which reflects the nature of objects exactly as they are as, without adding to them, without elaborating on them, without interpreting them through screens of subjective evaluation and commenting."
The term "mindfulness" (sati) does not mean 'non-thinking'. It means to 'remember' or 'keep in mind' (the factors of the eightfold path).
Mindfulness does not exclusively apply to the (non-judgmental) observation practise in the 7th factor of the eightfold path.
If right thinking (2nd factor of eightfold path) is practised, this is also an application of right mindfulness in Buddhism.
A (complex) quote below about how right mindfulness also applies to right thinking:
And what is the right resolve (thought) that is noble, without effluents, transcendent, a factor of the path? The thinking, directed thinking, resolve, mental fixity, mental transfixion, focused awareness & verbal fabricators in one developing the noble path whose mind is noble, whose mind is without effluents, who is fully possessed of the noble path. This is the right resolve that is noble, without effluents, transcendent, a factor of the path.
One makes an effort for the abandoning of wrong resolve & for entering right resolve: This is one's right effort. One is mindful to abandon wrong resolve & to enter & remain in right resolve (thought): This is one's right mindfulness. Thus these three qualities — right view, right effort & right mindfulness — run & circle around right resolve.